Amnesty, self-deportation, a wall. Politicians have plenty of ideas to fix America’s immigration system. But where does rhetoric leave reality?

PolitiFact and PunditFact have published more than 400 fact-checks dealing with immigration since 2007. Here are five myths we’ve heard.

Myth: 2016 GOP presidential candidates unanimously oppose a path to citizenship

"Not one" Republican candidate for President is clearly and consistently supporting a path to citizenship, Hillary Clinton said on a visit to a Nevada school in May 2015. While most aren’t, it turns out there is one who clearly is: Lindsey Graham. Graham has been upfront about his support for the policy as a member of the "Gang of Eight," a bipartisan group of Senators who drafted a comprehensive immigration reform bill in 2013. The bill was killed in the House, but Graham’s support for a path to citizenship remains.

While most GOP candidates haven’t supported a path to citizenship clearly and consistently, a slew of them have expressed support for it in the past, including Wisconsin Gov. Scott Walker, Ben Carson, Florida Sen. Marco Rubio, Former Florida Gov. Jeb Bush, Former Arkansas Gov. Mike Huckabee, and Louisiana Gov. Bobby Jindal. We rated Clinton’s claim Mostly False.

Myth: Obama has cut border security funding

Accusing President Barack Obama of failing to secure U.S. borders has become a common rallying cry among those seeking to crack down on illegal immigration, including 2016 presidential candidate Rick Perry

Way back in 2011, Perry, then the governor of Texas, claimed that the federal government "has not engaged in (protection of the border) at all." We rated his claim False; by the end of 2010, the federal government had invested almost $11.9 billion in border security, putting more than 40,000 troops on the ground.

In fact, Obama correctly stated in 2010 that the number of Border Patrol guards on duty in the Southwest had doubled in the previous six years. Is Obama open to amnesty? Yes. Is he lax on border security? The numbers suggest not.

Myth: Immigrants crossing the U.S.-Mexico border have criminal records, links to terror groups

It’s never good to generalize about a large group of people. Immigrants crossing the Southern border are no different.

Of the statements Donald Trump made in his 2016 campaign announcement, his false labelling of Mexican immigrants as "criminals" and "rapists" incensed both friends and foes of Trump’s. This isn’t a new claim; In 2014, we looked at a claim by then-Texas Lt. Gov. David Dewhurst that at "least a quarter of those apprehended" at the border "have criminal records."

Dewhurst’s numbers don’t quite line up: While his office told us that we had misinterpreted his statement, PolitiFact Texas found numbers provided by U.S. Immigration and Customs Enforcement that suggested that the number is closer to 1 in 20, or under 5 percent, and rated Dewhurst’s statement False.

Perry took this myth even further when, in an appearance on Fox & Friends, he mentioned that people crossing the border are "coming from states like Syria that have substantial connections back to terrorist regimes and terrorist operations." In 2013, Immigration and Customs Enforcement found only a handful of such cases: "2 from Nigeria, 3 from Pakistan, 1 from Egypt, 1 from Morocco and 1 from Afghanistan." Even if there had been more, it’s a big stretch to consider anyone from terrorism-affiliated countries a terrorist themselves. PolitiFact Texas rated Perry’s claim Pants on Fire.

Myth: The number of Mexican-born immigrants living in America is increasing

Another common myth is that the flow of people crossing the border has steadily increased in recent years, a misconception highlighted by conservative pundit Ann Coulter’s claim that the U.S. has already "taken in" about "one-quarter" of Mexico’s population, a number far higher than any previously reported.

While she pointed to a study by the Pew Research Center finding that about 33.5 million people of Mexican origin lived in the United States in 2011, Coulter’s analysis relies on the assumption that all 33.5 million are in fact from Mexico. In contrast to Mexico’s population of around 120 million, Coulter’s numbers seem to check out. But the number she found in the Pew study also includes around 20 million who are able to claim Mexican heritage but have never been considered residents of the U.S.’s southern neighbor. It was enough to earn her a Pants on Fire.

Rather, net immigration has been slowing in recent years. In fact, we rated Mostly True a claim by Bill Clinton that, from 2010 to 2014, there has been zero net in-migration across the Mexican border. While figures for 2014 have not yet been released, numbers from 2010 to 2013 show the number of Mexican-born American residents staying relatively constant at around 11.5 million, in one estimate actually falling by about 100,000. Fewer young people attempting to cross over to America and the allure of relative political stability in Mexico are just two of the factors behind this shift.

Myth: A majority of Americans will use Spanish as their first language by 2030.

Egged on by these bloated numbers, the looming prospect of a primarily Spanish-speaking nation incites fear in some and inspires others. But it’s probably farther off than we think. We checked out a quote from music-infused TV show Glee claiming that the U.S. Census predicted a majority of Americans would "use Spanish as their first language" by 2030.

While the Census Bureau predicts that by 2030 about 23 percent of Americans will be Hispanic, numbers from another Census study suggest that numbers of Spanish speakers will be much lower. As only about 13 to 15 percent of people over the age of 5 will use Spanish as their primary language by 2020, the study’s authors don’t expect that number to get anywhere near the 50 percent that Glee suggested. We rated that claim False.