Image copyright Thinkstock Image caption Only 4% of Fortune 500 companies, the largest corporations in the US, are run by women

Hillary Clinton has shattered a glass ceiling by becoming the first woman to be nominated for president by a major party in the US. She's now looking to shatter one more and become the United States' first female president.

But women are still fighting an uphill battle for equality.

Women are typically paid less, are under-represented in boardrooms and, as Marissa Mayer, Yahoo's chief executive recently pointed out, face bias in the media.

Yahoo recently announced a deal with Verizon to sell its core operating business for $4.8bn ($3.2bn), but on Monday Ms Mayer took a moment to address what she calls "gender-charged reporting".

She told the Financial Times: "I've tried to be gender blind and believe tech is a gender neutral zone but do think there has been gender-charged reporting.

"We all see the things that only plague women leaders, like articles that focus on their appearance, like Hillary Clinton sporting a new pantsuit.

"I think all women are aware of that, but I had hoped in 2015 and 2016 that I would see fewer articles like that. It's a shame."

Image copyright Getty Images Image caption Throughout her career Hilary Clinton has faced media security on her appearance including stories dedicated to the her pant suits

She's certainly not the first to make these points, but with the potential for the first woman president in the US and the UK now being led by its second female prime minister, the media will undoubtedly be covering female leaders even more.

Media coverage

At the heart of Ms Mayer's comments is the idea that women are judged in the media on their appearance, attitudes or families and that this in turn leads to judgements about their leadership.

Researchers at Kellogg business school in Illinois found that companies which appoint female chief executives and receive a lot of media attention see a decline in their share price.

Companies that appoint female bosses and don't receive a lot of attention are more likely to see a rise in their share price.

Image copyright Vogue Image caption Marissa Mayer was criticised for this photo that appeared in Vogue in 2013

Ned Smith, one of the study's authors, says this isn't necessarily sexism - it's speculation. Investors worry that others will react negatively to the news, so try to sell their shares before the stock price falls, creating a chain reaction that causes the stock to drop.

But when a company receives a lot of media coverage for appointing a male chief, its stock usually gets a boost.

Prof Smith said it doesn't appear that the coverage of new female chiefs is naturally biased, but because of how rare female chief executives are - just 1.5% of US public companies are headed by women - they receive three times more media coverage.

"As a society we want to know that companies are addressing this imbalance, but on the other hand, if that leads to speculative trading where investors assume everyone else is biased and trades accordingly, companies need to be aware of what might happen," says Prof Smith.

Parenthood and pregnancy

Image copyright Getty Images Image caption Ms Mayer received a lot of media attention for taking just two weeks' maternity leave

While his study focused on coverage of chief executive appointments it's also worth considering the impact of media coverage women executives receive throughout their time as leaders.

For example, after Ms Mayer announced her second pregnancy, the amount of coverage of her and Yahoo spiked and the company's share price sagged.

"As an investor you have to interpret the event and the meaning of all the buzz around that event, along with what others will think of it," says Prof Smith.

To take a different example, not too long after being appointed General Motor's chief executive in 2014, Mary Barra was asked in an interview whether she could be both a good mother and good boss and whether being a mother allowed her to give General Motors a softer image as it emerged from bankruptcy.

Image copyright Getty Images Image caption Mary Barra, GM's chief executive, has faced questions about her family and personal life that male bosses in her industry have not

One month later, when Mark Fields was appointed as the head of Ford, no journalist asked him whether his parenting skills would suffer as a result of his job.

Women in politics

Of course this isn't just a business issue. When Theresa May took over as Prime Minister, British newspapers ran wild with stories about her shoes.

A line in the Telegraph newspaper read: "Yes, Mrs May works a good shoe… but she doesn't flirt or use feminine wiles to get her way."

Hillary Clinton has faced similar scrutiny over wearing pantsuits and for "shouting" in her speeches.

A 2015 study commissioned by women's rights charity The Fawcett Society found that female politicians in the UK are often depicted more negatively than their male counterparts.

Image copyright Twitter Image caption Tweets by journalist also focused on female leaders shoes

"There is no reason what a woman was wearing should be a headline in a story over her achievements," says Polly Trenow, senior policy and campaigns officer for the Fawcett Society.

Gender imbalance

So, how should the problem be fixed? Should companies with female heads keep a low profile?

Does the public need to change its perception of female leadership, or should the media make a more conscious effort to become, as Ms Mayer put it, "gender blind"?

"The responsibility lies firmly at the door of the media, who should work to ensure that women's achievement and not just their looks are celebrated," says Ms Trenow.

With Mrs May and Ms Clinton, the media may have a chance to redeem itself.

But in Britain, parliament is still only 29% female, while the US Congress is even more gender imbalanced, just 19% of its politicians are female. Only 4% of Fortune 500 companies - the largest corporations in the US - are run by women.

All of which means that coverage of female leaders overall - biased or not - will still be the exception and not the rule.