Here is a breakdown.
In April 2001 the Netherlands became the first country in the world to allow gay and lesbian couples to marry in a civil ceremony.
Fifteen European countries have followed: Austria, Belgium, Britain (but not Northern Ireland, which only accepts civil partnerships), Denmark, Finland, France, Germany, Iceland, Ireland, Luxembourg, Malta, Norway, Portugal, Spain and Sweden.
Some European countries only allow same-sex couples to enter into civil partnerships including Croatia, Cyprus, the Czech Republic, Greece, Hungary, Italy and Switzerland.
In October 2014, Estonia became the first former Soviet republic to authorise this type of civil union.
Many eastern European countries -including Bulgaria, Latvia, Lithuania, Poland, Romania and Slovakia – deny homosexuals the right to marry or enter into unions.
In December 2015, Slovenians rejected in a referendum a proposal by their parliament to legalise gay marriage.
About 15 western European countries allow same-sex couples to adopt children, whether within marriage or civil partnerships. They include Belgium, Britain, Denmark, France, Germany, the Netherlands, Spain and Sweden.
Finland and Slovenia allow gay people to adopt their partner’s children.
Progress in the Americas
Canada led the way in North America, authorising same-sex marriage and adoptions in June 2005.
In the United States, a Supreme Court decision in June 2015 legalised gay marriage nationwide, at a time when it was illegal in 14 states.
Mexico’s federal capital was the pioneer in Latin America, authorising civil unions in 2007 and marriages in 2009 as well as adoption.
Same-sex marriages and adoptions are also legal in Argentina, Brazil, Colombia and Uruguay.
Chile’s socialist President Michelle Bachelet in August sent to congress a bill to authorise gay marriages and adoptions, after having legalised same-sex civil unions in 2015.
In Haiti, the Senate voted that same month to ban gay marriage.
Rare in Africa, Asia, Middle East
On the African continent, where around 30 countries ban homosexuality, gays can only legally marry and adopt children in South Africa.
Same-sex marriage has been legal in South Africa since the Civil Union Act came into force on 30 November 2006.
In the Middle East, Israel leads in terms of respect for homosexual rights, recognising gay marriages performed elsewhere although such unions are not allowed in the country itself. Gay couples can adopt children.
In the Asia-Pacific region Taiwan is set to legalise same-sex unions after its highest court in May ordered parliament to amend relevant laws within two years.
New Zealand passed a law in April 2013 legalising gay marriage and adoptions.
And on Thursday Australia’s lower house of parliament overwhelmingly voted in favour of gay marriage, which can take place early next year. Gay adoption is allowed.