Swedish prosecutors issued a European arrest warrant for Mr Assange after allegations of sexual assault related to a 2010 visit Mr Assange made to Stockholm to give a lecture. He denies the claims.
These are the key dates:
Below is more information on how events have unfolded:
Julian Assange arrives in Sweden on a speaking trip partly arranged by "Miss A", a member of the Christian Association of Social Democrats. He has not met "Miss A" before but reports suggest they have arranged in advance that he can stay in her apartment while she is out of town for a few days.
"Miss A" and Mr Assange attend a seminar by the Social Democrats' Brotherhood Movement on "War and the role of media", at which the Wikileaks founder is the key speaker. The two reportedly have sex that night.
Mr Assange reportedly has sex with a woman he met at the seminar on 14 August, identified as "Miss W".
Some time between 17 and 20 August, "Miss W" and "Miss A" are in contact and apparently share with a journalist the concerns they have about aspects of their respective sexual encounters with Mr Assange.
Mr Assange applies for a residence permit to live and work in Sweden. He hopes to create a base for Wikileaks there, because of the country's laws protecting whistle-blowers.
The Swedish Prosecutor's Office issues an arrest warrant for Mr Assange on allegations of rape and molestation.
Both women reportedly say that what started as consensual sex became non-consensual.
Wikileaks quotes Mr Assange as saying the accusations are "without basis" and that their appearance "at this moment is deeply disturbing". A later message on the Wikileaks Twitter feed says the group has been warned to expect "dirty tricks".
The arrest warrant is withdrawn. "I don't think there is reason to suspect that he has committed rape," says one of Stockholm's chief prosecutors, Eva Finne.
Prosecutors say the investigation into the molestation allegation will continue but it is not a serious enough crime for an arrest warrant.
The lawyer for the two women, Claes Borgstrom, lodges an appeal to a special department in the public prosecutions office.
Mr Assange is questioned by police in Stockholm and formally told of the allegations against him, according to his lawyer at the time, Leif Silbersky. The activist denies the allegations.
Swedish Director of Prosecution Marianne Nye says she is reopening the rape investigation against Mr Assange. "Considering information available at present, my judgement is that the classification of the crime is rape."
The Wikileaks founder is denied residency in Sweden. No reason is given, although an official on Sweden's Migration Board tells the AFP news agency "he did not fulfil the requirements".
Stockholm District Court approves a request to detain Mr Assange for questioning on suspicion of rape, sexual molestation and unlawful coercion. Ms Nye says he has not been available for questioning.
By this time Mr Assange has travelled to London. His British lawyer, Mark Stephens, says his client offered to be interviewed at the Swedish embassy in London or Scotland Yard or via video link. He accuses Ms Nye of "abusing her powers" in insisting that Mr Assange return to Sweden.
Swedish police issue an international arrest warrant for Mr Assange via Interpol.
The Wikileaks founder gives himself up to British police and is taken to an extradition hearing. He is remanded in custody pending another hearing.
Mr Assange is granted bail by at the High Court and is freed after his supporters pay Â£240,000 in cash and sureties.
A British court rules that Mr Assange should be extradited to Sweden.
Lawyers lodge papers at the High Court for an appeal against extradition.
The High Court upholds the decision to extradite Mr Assange .
Mr Assange wins the right to petition the UK Supreme Court directly after judges rule that his case raised "a question of general public importance".
The Supreme Court rules that he should be extradited to Sweden.
Ecuador's foreign minister says Mr Assange has applied for political asylum at Ecuador's embassy in London.
Ecuador's foreign minister claims the UK has issued a "threat" to enter the Ecuadorean embassy in London to arrest Mr Assange. The Foreign Office says it reminded Ecuador that it has the power to revoke the diplomatic immunity of an embassy on UK soil and says Britain has a legal obligation to extradite him.
Ecuador grants asylum to Mr Assange, saying there are fears his human rights might be violated if he is extradited. Mr Assange describes it as a "significant victory", but the UK government expresses its disappointment.
The UK insists it will not grant Mr Assange "safe passage" to Ecuador as it seeks a diplomatic solution. Downing Street says the government is legally obliged to extradite him to Sweden.
Nine people who put up bail sureties for Mr Assange are ordered by a judge to pay thousands of pounds each after his failure to appear in court.
Ecuador's ambassador says Mr Assange has a chronic lung infection "which could get worse at any moment". The embassy says it sought assurances Mr Assange would not be arrested if he was taken to hospital.
Mr Assange says he will leave London's Ecuadorean embassy "soon" after two years of refuge. He does not clarify when he will depart but says it is "probably not" for the reasons reported in the UK press. Stories had suggested he required medical treatment.
Swedish prosecutors drop their investigation into one accusation of sexual molestation and one of unlawful coercion against Mr Assange because they have run out of time to question him. The more serious allegation of rape is not due to expire until 2020.
Scotland Yard announces it will no longer be sending officers to stand guard outside the Ecuadorean embassy in London. Officers had been there since 2012, at an estimated cost of more than Â£12m.
The Metropolitan Police says the effort is "no longer believed proportionate" but it would be deploying "a number of overt and covert tactics to arrest" Mr Assange.
A UN panel rules that Mr Assange should be allowed to walk free and be compensated for his "deprivation of liberty".
The UN's Working Group on Arbitrary Detention says the Wikileaks founder was arbitrarily detained by UK and Swedish authorities since his arrest in 2010, and the detention violated his human, civil and political rights.
Mr Assange hails it a "significant victory" and calls the decision "binding" - but UK Foreign Secretary Philip Hammond brands the ruling "ridiculous".
The UK Foreign Office says the report "changes nothing" and it will "formally contest the working group's opinion".
Before the ruling, police said he would still be arrested if he left the embassy.
Wikileaks co-founder Julian Assange has been holed up in the Ecuadorean embassy in London since 2012, after seeking asylum there in his bid to avoid extradition to Sweden on a rape allegation.