LGBT rights are the major civil-rights push of the times, and at least stateside, the results are starting to show, most notably through the end of Don't Ask Don't Tell and gay marriage being slowly- very slowly- legalized state by state.
But that's in the United States. Compared to other places, the fight here is easy. You'll see at Wikipedia a chart of countries by the LGBT rights they do or do not have, and in over 80 countries, homosexual activity is illegal, sometimes punishable by death. A map is also there for reference. In those countries, the tide of LGBT rights is often going in the other direction entirely, most notably in Uganda.
These places are the ones now on the radar of the Human Dignity Trust, based in the United Kingdom, which tomorrow in the House of Lords is kicking off an effort to challenge anti-gay legislation in every country where it's illegal, starting in Belize. They intend to do this through pointing to international law- the 1994 UN Human Rights Committee case Toonen v. Australia figures to see prominent play- and by using local talent wherever they can. Caleb Orozco will head the case in Belize, which is intended as a test case, along with Jamaica (headed by Maurice Tomlinson) and Northern Cyprus (head there not found), intended to be brought by the end of the year. Essentially, the easier cases are getting priority; the hope is that wins in those places will intimidate some of the more entrenched nations, such as Cameroon, into decriminalizing it on their own rather than have their hands forced in court. If need be, the HDT is prepared to bring cases themselves.
The United Kingdom being the home of the lead actors here is a coincidence,
but not very much of one. About half the countries targeted are part of the Commonwealth of Nations, an organization of countries holding a historical connection to the British Empire (the United States is not part of it), and in the Empire's heyday, homosexuality was illegal, a policy exported to its subjects and only decriminalized in Britain in 1967. The HDT, among its other aims, feels a sense of obligation to undo the damage the British exported.
The HDT stresses that they don't intend to go any further than that; they won't be doing any gay-marriage cases. There isn't enough international case law to fight that fight. They just are aiming for decriminalization.
And let's hope they get it.