Their daughter Aarushi and their help Hemraj were found murdered in their Noida home in 2008.
The Talwars were convicted of the murders.
There were however many large question marks over both the investigation and the conviction, with numerous accusations of them having been botched.
A total of three teams had investigated the murders.
The Uttar Pradesh police had first announced that Aarushi, who was 14 at the time, and Hemraj were found in a "compromising position" which is why her parents had killed them in a fit of rage.
The investigation was then taken over by first one CBI team and then another.
The Central Bureau of Investigation also worked along the same lines -- that Aarushi and Hemraj had been caught in the sexual act by her parents.
A special CBI court in Ghaziabad convicted Rajesh and Nupur in 2013 and sentenced them to life imprisonment.
The Allahabad High Court -- which overturned their conviction last Thursday, the Talwars had appealed -- had lambasted the CBI court for its conviction, and the CBI for its investigation.
The high court said the CBI had tutored witnesses, that a conviction cannot be based on "mere suspicion", and that the Talwars had to be given the benefit of the doubt.
And it rubbished the theory that Aarushi and Hemraj had been caught in the sexual act.
"We have no hesitation in holding that the prosecution has failed to prove by any reliable or cogent evidence, the motive suggested by the prosecution for the appellants to commit the double murder i.e. the deceased being caught in the midst of a sexual act on the fateful night by Dr. Rajesh Talwar who suddenly got so gravely provoked that he committed their murder," the high court had said.