It can be hard to keep track of all the twists and turns that the investigation has taken with seemingly countless theories as to who or what may have been behind the assassination of one of the nation's most controversial political figures.
The police have archived so much material that their stack of files could stretch two-thirds of the way up the Empire State building. Some 130 people have even confessed to killing Palme. And 25 years after the fact, people are still ringing up the police with tips.
So, why don't we know yet who murdered Olof Palme?
"If I knew the answer to that, then maybe we would have found the killer already," Kerstin Skarp, the prosecutor on the Palme case for more than a decade, tells Radio Sweden.
"It's hard to know what it depends on – if we did something wrong, or if we didn't get the crucial information, or if we didn't have the luck that sometimes one needs. There can be quite a number of factors," says Skarp.
Standing at the scene of the crime in the heart of Stockholm, Kerstin Vinterhed, author of the new book MURDER, says the investigation was botched from the start.
"It took, I think, two hours before there was an alarm all over the country to watch out," says Vinterhed. "The place was not surrounded – it immediately should have been shut off from the public and so on. So, there were a lot of mistakes from the very beginning, and then the investigation of the murder also went astray."
Shortly after the murder, police arrested a suspect known in Swedish newspapers as "the 33-year-old". But he was soon set free and suspicions turned elsewhere.
The first police investigator on the case, Hans Holmér, soon got sidetracked by a conspiracy theory that the Kurdistan Workers Party was somehow behind the murder.
"Instead of trying to find out who had been on the spot and trying to solve it in that way, they concentrated on a conspiracy that was just a fantasy," says Vinterhed. "That, of course, is their main mistake."
"After those first two confused years, (the polices') slogan was 'back to Sveavägen', back to the place of the crime," says Vinterhed.
That led to the arrest and conviction of Christer Petterson in the summer of 1989, but a few months later, an appeals court overturned the ruling based on a lack of technical evidence and let Petterson off.
Over the years, both the police and the Swedish people have grappled with a host of theories, ranging from the Middle East to South Africa to Yugoslavia to private persons. But none of them can hold water unless the police can prove that the murderer could have been at the scene of the crime when it happened.
"What everyone says who is really initiated here is that it can never be solved," says Vinterhed, "because the main suspect, who is still Christer Petterson even though he was released, he is dead. And the weapon has never been found. So, you can't solve this murder. You will never be able to do that."
But when Radio Sweden asks prosecutor Kerstin Skarp if it is still possible for the case to be solved, she says:
"One can answer very easily, and say it's because there's no statute of limitations for the case (anymore). Someone has demonstrably committed the crime, and so long as we haven't found who it is, there is a chance – a theoretical chance, in any case – to find out who it was.
"And we certainly have quite a lot of material here. If something comes in, there's a good chance that it's a puzzel piece to something that we already have here. So, that's why I feel that one should – I can't say now that we will solve it, but I'd rather never say that we won't solve it."
Until recently, the Swedish statute of limitations for murder was 25 years, which meant that the investigation would have been forced to end today. But a recent change in the law got rid of the restriction, which means that technically, the investigation can go on forever. This doesn't mean that people want it to though.
A new opinion survey by the newspaper Svenska Dagbladet and Sifo paints the picture of exhaustion: only 5 percent of Swedes believe that the investigation might at some point lead to a conviction. And more than half of Swedes say it's time to close the file forever and move on.
"It's been said that Sweden lost its innocence when this happened, and I think there is some truth in that," says Vinterhed.