Olof Palme was shot dead on the street of Sveavägen in Stockholm as he and his wife were walking home from the cinema on the 28th of February 1986.
Thirty years on, the police is no-where near proving who killed him, and the murder investigation continues. Earlier this week, the investigators part of the police's "Palme group" held a press conference to give an update of its work.
And while the once much publicised sketch of a possible suspect, based on one woman's witness statement, was officially dismissed as having done more damage than good to the investigation, the so called South Africa lead is among those deemed to still is interesting by the group.
This line of inquiry is based on the idea that people in the then South African intelligence and security service were behind the murder.
"Lately we have been geting quite a lot new material, partly from journalists who have been to South Africa and spoken to people in the authorities there. Also from a previous diplomat who was working at the embassy in Pretoria has shed new light on Palme's involvement in the anti-apartheid movement. We have also been given a lot of information from the aid agency Sida, and this information means that we have to go through the South Africa lead again, to see if there are further steps we can take there," said Dag Andersson, who is in charge of the six-man-team "The Palme Group".
Another line of inquiry that is also still "live" is related to the many witnesses that have seen people using walkie-talkies near the crime scene on the night of the murder.
"There are about 80 such observations. I think that is far too many to not take it highly seriously. There are people who - independent of each other - have made observations at the same time, and even though the description of these people often differ, there are also similarities," said Andersson.
But the theory that there was a group of right-wing police officers who conspired to kill the prime minister was dismissed at the press conference, by prosecutor Kerstin Skarp, who said there is no such line of inquiry.
"There is a whole bunch of loosely connected information about how different police officers acted, but they are not registered in anyway under something known as the 'police theory'," she said.
That the initial police investigation was a shambles is widely accepted today, and the number of mistakes made even in the initial stages has baffled many over the years. For example, it took a long time before the area around the murder scene was properly cordoned off.
The only proper evidence from the crime scene is two 357 Magnum Winchester Western metal piercing bullets. At the press conference this week, the investigators said they are interested in hearing from anyone who may have information about a Smith & Wesson Magnum revolver owned at the time by a man, now deceased, who hated Palme.
To some people, including Olof Palme's own family, the murderer has already been found. In 1989, the drug addict and alcoholic Christer Pettersson was convicted by a district court for the murder. Among the evidence against him was the statement from Lisbet Palme, Olof's wife, who picked him out from a police line-up as the one she had seen at close range shooting her husband.
But the case did not hold up in the appeal court, partly because of mistakes made in connection with the line-up.
Nevertheless, Christer Pettersson continued to be of interest to the investigators, and as late as 1998 the case was appealed again, but the supreme court deemed that the new evidence was not sufficient to re-open the case. Pettersson died in 2004.
Asked this week how he felt about the murder investigation and the different theories about who did it, Olof Palme's oldest son Joakim told Swedish Radio News that as far as he is concerned, the murder has already been solved.
"The difficulty is that there are many possible scenarios, many possible conspiracies behind the murder, not least international ones. South Africa, the Chilean security service, extreme Palestinian movements and in Sweden there were also others who devoted themselves to political violence during this period," he said.
"But for me, these theories are not interesting as long as you cannot connect them to the observations at Sveavägen. And it has not been possible to do that. And my starting point is that if you are going to decide who fired the shot, you need to get down to Sveavägen and then there are strong witness statements against Christer Pettersson, including that of my mother's, but also from other people who have been there," he said.
In the interview, Joakim Palme, who is now one year younger than his father was when he was killed, says each anniversary brings with it a lot of attention.
"It can be overwhelming... but I think it has been interesting to see that his life and achievements have been more in focus in the later years, and not just the murder investigation that for a long period has dominated so completely," he says.
Over the last few years, several new documentaries and biographies have been published that have tried to paint a fuller picture of Olof Palme and of Sweden during his years in politics. Asked what he as his son feels is Olof Palme's most important political legacy, Joakim Palme hesitates.
"I think it is difficult to emphasise anything in particular but, with hindsight, perhaps the education area, where he investigated and designed the student financing that still is up and running today," he says.
He also mentions gender equality as another area where Palme made a difference: pushing for the expansion of childcare provision and new rules that meant husbands and wives began being taxed independently from each other, which encouraged many women onto the labour market.
"Back then it was controversial but now even (a conservative moderate like) Fredrik Reinfeldt can make propaganda for the Swedish model when he goes to visit the (UK Prime Minister) David Cameron. So of course, some of that was Social Democratic policies, but others were just part of modernising Sweden," says Joakim Palme.