By Rupert Wingfield-Hayes
BBC News, Moscow
Ms Politkovskaya was shot dead in her Moscow apartment building in 2006
From the start, the trial that ended on Thursday in Moscow was not, as some media have dubbed it, the "murder trial of Anna Politkovskaya".
None of the three defendants, Dzhabrail and Ibragim Makhmudov or Sergei Khadzhikurbanov, was ever accused of her murder.
If they had been found guilty, it would not have resolved the fundamental question of who killed Anna Politkovskaya, or the even more important question, who ordered her killing.
It would equally be wrong to say that the acquittal of the three men is a calamity for Russian justice.
The whole case, from start to finish, has been a calamity, critics say.
As the three men walked free from the military court, there was one point that almost everyone agreed on - the investigation into Anna Politkovskaya's murder had been a fiasco.
Two Chechen brothers were among three men acquitted in the trial
The question that many are asking is: was it incompetence or a conspiracy?
In other words, they ask, did the investigation fail because the Russian police are useless, or because powerful people wanted it to fail?
In the murky world of Russian politics it is hard to be sure why events have unfolded in the way they have.
What is known is that on 7 November 2006, Anna Politkovskaya was shot dead in the lobby of her apartment building in central Moscow.
The murder carried all the hallmarks of a contract killing. She was shot five times in the head and chest.
Ms Politkovskaya had been a fierce critic of the Kremlin, of President Vladmir Putin, of government corruption and of the stifling of political freedoms in Russia.
But her most outspoken writing was on the war in Chechnya.
Her reporting on the terrible human rights abuses there made her many enemies both in the Russian security forces and the pro-Moscow militias.
When 10 men were arrested in August 2007, it appeared to confirm everybody's suspicions. It painted a disturbing picture of gangsters and security agents working together to carry out contract killings.
Ms Politkovskaya's children will likely never know who killed their mother
It also appeared to confirm a Chechen connection.
Investigators alleged that the contract for Ms Politkovskaya's killing came from a Chechen gangster.
He allegedly passed it to a former Moscow police officer, who is then said to have brought in a member of the state security service, the FSB, to help him arrange the killing.
Finally three Chechen brothers were allegedly hired to carry out the hit.
But the investigation was also plagued by mistakes, incompetence, and, some would say, deliberate sabotage.
The alleged killer was somehow tipped off and was able to flee the country.
And it has never emerged why Anna Politkovskaya had been under surveillance by the FSB for at least two months before her murder.
Very quickly the investigation ground to a halt.
Ms Politkovskaya has become a cause celebre around the world
As soon as it became clear that the FSB was involved, a veil of secrecy descended.
In the end only three men were charged, and not directly with the murder.
When the trial finally opened, it was, for no clear reason, held in a military court.
For three months it stuttered on. The evidence presented was circumstantial at best. In the end the jurors were unconvinced.
There are many theories as to who really ordered Anna Politkovskaya's murder.
Most point to the pro-Kremlin militias in Chechnya, and in particular, to Chechnya's warlord president Ramzan Kadyrov, who has repeatedly denied the accusation.
It seems very unlikely that we will ever find out the truth.