This movie is very engaging, even though it was made in early 30's. Eight children has been missing in a German town (I believe it's Düsseldorf, since in several countries the movie is called M The Vampire of Dusseldorf). The police has been looking for the killer (the children are presumably dead) for 8 months without finding a single hint. Then the killer sends a letter to the police, and that is where the police get their first clue. They do find the killer's apartment.
In order to find the killer which terrorizes the town, the police swarm the city. The criminals feel they can't move freely and decide to catch the murderer. They use beggars to watch every children. Finally, a balloon seller recognizes the murderer - who whistles In der Halle des Bergkönigs from Peer Gynt - who is soon marked with a letter "M" (Mörder /Murderer) with a chalk. Knowing that he is being followed, M hides in an office building, but the criminals won't give up and raid the building, catch him, and put him before a kangaroo trial.
M suffers a mental illness. If he is tried in a government's court, will he be set free and sent to an asylum instead? Will there be justice to the parents of the lost children? Must M alone bear the responsibility? It is mentioned that M is a former patient of an insane asylum. The doctor who let him go, doesn't he have a moral responsibility, too, to the 8 lost children? If the doctor has decided that M is no longer a danger to the society, but knows if by nature he is a threat, why not put a watch over him? And the parents are also guilty, like the mother say in the end of the movie: "We should keep a closer watch on our children."