Actress Laverne Cox has dazzled viewers as transgender prison inmate Sophia Burset on Orange is the New Black. Many of the accolades come from the trans community, as Cox's work as Sophia has raised awareness about casting trans performers as trans characters. While performers including Candis Cayne, Calpernia Addams, and Harmony Santana have won film and television roles in the past, these casting choices are rare.
What television and film audiences usually see are cisgender men and women performing as a trans characters. Sometimes these roles are played for laughs, sometimes not. Often, trans women are portrayed as hyper-feminized versions of women, with exaggerated makeup, wardrobe, or mannerisms. In the case of male actors playing trans women this is especially problematic, as it can provide ammunition for people who claim that trans women are just like drag queens, another kind of men in dresses. Some people suggest that acting is acting, and make the comparison of straight actors playing gay men or women (and vice versa), but the fact is that a trans woman is a woman, and a trans man is a man. Despite the increasing availability of trans performers, trans people are frequently played by cisgender actors, and far too often by performers of the wrong gender.
Here's a roughly chronological sampling of 21 times this has happened.