We have a US president who supports gay marriage, and now a pope who, if not exactly signing up to equality for all, is at least starting to talk in language less inflammatory than his predecessor. "If someone is gay and he searches for the Lord and has goodwill, who am I to judge?" he told an assembled group of journalists on the papal plane back from his tour of Brazil. Then he went on to criticise the gay "lobby" and said he wasn't going to break with the catechism that said "homosexual acts are intrinsically disordered". Still, for a brief moment it looked like a minor breakthrough.

Then you weigh it against a raft of anti-homosexuality legislation that is coming into force in countries across the world. In Russia, gay teenagers are being tortured and forcibly outed on the internet against a backdrop of laws that look completely out of step with the rest of Europe. In what is being described as rolling the "status of LGBT [lesbian, gay, bisexual and transgender] people back to the Stalin era", President Putin has passed a number of anti-gay laws, including legislation that punishes people and groups that distribute information considered "propaganda of non-traditional sexual relations". The country also now has powers to arrest and detain foreign citizens believe to be gay, or "pro-gay". It has led to the boycott of Russian vodka brands by gay bars and clubs in solidarity, started by writer and activist Dan Savage and taken up by bars in London.

In many African countries where homosexuality is already illegal, more draconian anti-gay laws are being passed and violence against LGBT people is increasing.

Is there a link between growing rights in some countries and worsening or removal of rights in others? "There are really complicated links between the two. If you look at the history of the advancement of LGBT rights in the UK, every advance is accompanied by a backlash," says Alistair Stewart, assistant director of the Kaleidoscope Trust, a UK-based organisation that supports international LGBT rights. "To a certain extent that's happening on a global scale now – the advances that are being made in some parts of the world encourage a backlash in other parts of the world. The struggle for even basic human rights for LGBT people – freedom of association, freedom from violence – becomes harder to achieve when the opponents can point to something like gay marriage, which isn't even on the books for most of the countries we're talking about and make the argument that 'if we give these people even the most basic of human rights, next they'll be asking to get married in our churches'." Jonathan Cooper, chief executive of the Human Dignity Trust, is less sure they are related: "The further persecution is already happening."

The Human Dignity Trust challenges laws to end the persecution of LGBT people around the world. "Most countries sign up to international human rights treaties. If you take Belize as an example, it has ratified all the key UN human rights treaties and in their constitution they have a right to a private life, to equality, to dignity. And so basically to criminalise homosexuality is a violation. To bring a legal challenge against that takes a very brave individual." It has been supporting Caleb Orozco, the gay rights campaigner who launched a legal challenge to overturn Belize's criminalisation laws. "We're still waiting for the judgment. They said it would be out by the end of July but obviously it's not coming now."

Orozco's case has prompted a backlash in Belize against him, and Unibam (the United Belize Advocacy Movement). A report last week from the Southern Poverty Law Center, the US civil rights organisation, highlighted the influence US hardline religious groups had in Belize and other countries. "Many of these American religious-right groups know they have lost the battle against LGBT rights in the US, and they're now aiding and abetting anti-LGBT forces in countries where anti-gay violence is prevalent," said Heidi Beirich, author of the report. "These groups are pouring fuel on an exceedingly volatile fire."

It's the classic missionary model, says Stewart, "where money and resources and organisation are set up in the countries that they are targeting". It's also worth remembering which country is responsible for the legacy of persecution faced by millions of LGBT people today. There are more than 75 countries where homosexuality is still criminalised: "Forty-two of them are former British colonies so we can see where the legacy comes from," says Cooper. To see which countries are getting worse in terms of gay rights makes grim reading, but Stewart is cheered by the support he sees. "One of the reassuring things that has come out of the response to the Russian laws in particular is there is a growing international apprehension. One of the last great undone pieces of the civil rights movement is to address the rights of LGBT people, and there does seem to be a growing international support for change."

Where are LGBT rights improving?



Parts of Latin America remain the standard for equality for LGBT rights. Argentina's Gender Identity Law 2012 allowed the change of gender on birth certificates for transgender people. It also legalised same-sex marriage in 2010, giving same-sex couples the same rights as opposite-sex couples, including the right to adopt children. Uruguay and Mexico City also allow equal marriage and adoption, and last week Colombia recognised its first legal same-sex civil union (not "marriage").

In Asia, LGBT groups are making progess, if slowly. Last year, Vietnam saw its first gay pride rally and this year's event will launch a campaign for equality in employment. On Tuesday, it was reported that the country's ministry of justice has backed plans to legalise gay marriage, after the ministry of health came out for marriage equality in April.

In Singapore the Pink Dot pride rally attracted 21,000 people at the end of June – its biggest number since it started four years ago. "It's a strong signal that Singapore is not as conservative as some think," Paerin Choa, a rally spokesman, told Reuters. Just hours before attending the rally, Vincent Wijeysingha became Singapore's first openly gay politician when he officially came out. The country bans gay sex, though this is rarely enforced, but in April a gay couple, Gary Lim and Kenneth Chee, attempted to get the law removed. Their case was dismissed, but they are appealing with the help of Lord Goldsmith, the former attorney general.

The Human Dignity Trust filed a suit at the European court of human rights against Turkish-occupied northern Cyprus, the only place in Europe where homosexuality is still illegal, and looks likely to win.

In a letter sent to the Kaleidoscope Trust, the prime minister of Trinidad and Tobago expressed her wish to repeal the laws that ban homosexuality. The prime minister of Jamaica, Portia Simpson Miller, has voiced similar wishes. In June, Javed Jaghai was the lastest activist to launch legal proceedings to challenge the anti-sodomy laws (however, violence against gay people is increasing, and 17-year-old Dwayne Jones was stabbed to death last week at a party according to local media reports).

In Malawi, the president Joyce Banda announced in 2012 that laws criminalising homosexuality would be repealed – she has since distanced herself from that, although there has been a moratorium and there have been no prosecutions. "So it's not just the global north where things are moving forward. In some parts of the world where you'd least expect them, things are getting better," says Stewart.

The number of countries legalising same-sex marriage continues to grow, with Denmark, Brazil, France and New Zealand just some that joined more progressive countries that had legalised it earlier. Last month in the US, where Barack Obama publicly supports equal marriage and it is legal in several states, the supreme court struck down the Defense of Marriage Act (which prevented the federal government from recognising marriages between gay couples) as unconstitutional. And of course England and Wales now has the Marriage (Same Sex Couples) Act 2013.

Where are LGBT rights worsening?



In Iran, a place where homosexuality is punishable by death and you thought LGBT rights couldn't really get worse, this year the country's official who works on human rights described homosexuality as "an illness that should be cured". Of course, gay rights are no better in many other Middle Eastern countries. The ILGA (International Lesbian, Gay, Bisexual, Trans and Intersex Association) provides a comprehensive look at state-sponsored homophobia in a 2013 report.

Gay-rights activist Yury Gavrikov is detained by riot police at a rally in Moscow in May. Photograph: Kirill Kudryavtsev/AFP/Getty Images

Two weeks ago, Eric Ohena Lembembe, was found at home in Yaoundé, the capital of Cameroon. He had been tortured – his neck and feet broken, his body burned with an iron – and murdered. As the executive director of Camfaids, Lembembe was one of Cameroon's most prominent and outspoken LGBT rights activists and openly gay – an astonishing act of bravery in a country where homosexuality is punishable with prison and violence against LGBT people is common and almost never investigated. Amnesty International's 2013 report on global human rights stated even people who supported LGBT rights were being harrassed, particularly equality lawyers Alice Nkom and Michel Togue who had both received calls and text messages threatening to kill them and their children if they did not stop defending gay people who had been arrested. In June this year, Togue's office was broken into and files and computers stolen. In March 2012, a workshop held to educate young people about LGBT issues was shut down.

Last week, two men were given prison sentences under the country's anti-gay laws; in 2011, another man, Jean-Claude Roger Mbédé, was sentenced to three years in prison for sending a text message to another man. Men who are perceived to be gay are arrested, somtimes only on the basis of someone's suspicions, and some are forced to undergo rectal examinations and tortured into confessing. "They have such an active prosecution system," says Cooper. "Although prosecutions do occur in other jurisdictions, you don't have that kind of active prosecution policy that you have in Cameroon."

After the death of Lembembe, gay-rights groups said they couldn't continue their work unless they are given protection by international donors who fund the fight against HIV/Aids. "We have all decided to stop our work in the field because our security is at risk," said Yves Yomb, executive director of Alternatives-Cameroun. "We have no protection from the police and we feel that our lives are at risk."

Sharing a border with Cameroon, Nigeria's anti-gay laws are becoming ever more draconian. It recently passed a bill outlawing same-sex marriage, punishable with a 14-year prison term. "Nobody in the country is seriously asking for gay marriage," says Stewart from the Kaleidoscope Trust. "There is no reason to legislate against it, when homosexual sex is already illegal. It also has more concerning provisions that ban the formation of groups that support LGBT rights and a series of provisions that if you know a homosexual but don't turn them in, you are aiding and abetting. That isn't on the statute books yet but it seems likely that it will pass in some form."

Politicians in Uganda are attempting to pass a similar bill, at one point seeking to punish homosexual relationships with the death penalty; people found guilty of being gay will now face life imprisonment, and anybody – parents, teachers, doctors – who suspects someone in their care is gay will be punished if they do not report them.

Last week, President Mugabe told a rally of Zanu PF supporters that Zimbabwe would never accept homosexuality, and that gay people were "worse than pigs, goats and birds". There are 38 African countries where homosexuality is illegal.

In Russia, gay rights are moving further away from other European countries. In an extreme version of Britain's section 28, a new law will punish anybody disseminating "propaganda of non-traditional sexual relations among minors expressed in distribution of information … aimed at the formation … of … misperceptions of the social equivalence of traditional and non-traditional sexual relations". It has also failed to comply with the 2010 judgment at the European court of human rights that requires it to allow gay pride events. Violence against LGBT people is rising. In May, there was a brutal murder of a man who had revealed to "friends" he was gay. Official numbers of homophobic attacks are low, but LGBT activists say this is because attacks are not often reported, and when they are police rarely label them as such, but one poll last year of nearly 900 people by the Russian LGBT Network found more than 15% had experienced physical violence between November 2011 and August 2012.

Last week, the Pink News reported neo-Nazi groups in Russia has been luring gay teenagers to meetings, where they are forced to come out in videos that are then posted on social media sites. It reported that one victim, 19-year-old Alex Bulygin, killed himself after his sexuality was revealed.

Russia's renewed attacks on homosexuality may be spreading beyond its borders – there are moves in Ukraine to adopt its own ban on "gay propaganda" and in May the parliament dropped a bill that would have outlawed discrimination on the basis of sexual orientation after a protest by anti-gay activists.

• This article was amended on 31 July 2013. A reference to the timing of a Belize judgment was removed.