Martin Beck is the head of the homicide unit, and the stories generally follow him around. But it is a feature of the series - unlike, say, Simenon's 'Maigret' stories - that the unit is presented as a real workplace. The continuing characters are a group of detectives whose lives and interactions with each other are part of the story, and can be part of the problem to be solved. Further, the unit is set in its bureaucratic context, with sometimes tense relationships with higher authorities.
And that, surprisingly, is a key to the impact of the books. The whole series has a title, 'The Story of a Crime', and this 'crime' is a political one. It is the destruction of community-based policing, the national centralization of the Swedish police force, and its transformation into an armed, almost paramilitary, force. The series makes a sustained and powerful critique of policing, including brutality, abuse of power (memorably in The Abominable Man), incompetent management, incipient fascism, and a slow but devastating separation from the people whom the police are supposed to be serving. And that becomes a critique of the increasingly conservative social-democratic regime that ruled Sweden at this time.
This all sounds grim, but these books are not depressing. They are lively stories with well-defined characters, plenty of humour, realistic and well-described settings. Translation probably weakens their impact, but I have always found them books to cherish - and to learn from.