One of the pleasures readers derive from translated crime novels is beginning to feel at home in a foreign place. For example, consider how much we have all learnt about Scandinavian countries from their revelatory fiction or about Sicily from Montalbano’s adventures there. A complete list would be very long; recently added to it is Barcelona, from which Antonio Hill is sending intricate and interesting dispatches. Inspector Héctor Salgado appears for the second time in what I hope will turn out to be a long-running series. In this episode he is investigating a run of suicides by the senior staff of a local cosmetics manufacturer. Simultaneously his assistant, supposed to be away on maternity leave, is continuing an unsuccessful investigation into the disappearance of the mother of Salgado’s son. All these people seem very real, as does the city in which they live. Salgado himself is an interesting, sympathetic character with a complicated history, and Hill is very good at making the personal details that bring a fictional hero to life relevant to the story he is telling.

Sometimes a crime strikes the public imagination and is remembered whether or not its perpetrator is identified and punished. In The Detective’s Daughter, the murder of a young mother is such a crime, remembered thirty years later by Stella Darnell, the daughter of the detective inspector who tried and failed to identify the culprit. Stella had always resented her father’s obsessive preoccupation with that particular crime. After his sudden death she comes across the case papers in his attic and finds herself not only reading through them but caught up in the mystery itself. With the same methodical thoroughness that she uses for running her cleaning agency, Stella sets out to solve her father’s last case. The rest of the story is neatly worked out – this book has a clever mystery plot – but its excellence is in the characters, all credible and memorable, and in its setting in a real west London street, exactly described.

Italy has several different police forces. Detective-Colonel Piola and Captain Katerina Tapo are carabinieri, answerable to the Ministry of Defence and at permanent war with civilian police such as Donna Leon’s Commissario Brunetti. But we are inevitably reminded of him as an investigation is conducted in the familiar Venetian setting of alleys and canals. The case begins with a single corpse floating in the lagoon, and culminates in high politics and war crimes, by way of medieval superstition, religious prejudice and some justifiably belligerent feminism. The city is still beautiful and magical, but only superficially, for ‘crime has taken over Venice. It was like a parasite, the sort that feeds on its host, and weakens it without ever quite killing it. Most of the time it was invisible but if you knew how to see it, it was there.’ The corruption of Italy’s civil society is one of the themes of this novel, but so is a much more dangerous corruption that goes to the heart of American society, and of the American army that effectively occupies parts of Italy. It’s rare to find a genuinely thrilling thriller that is also an illuminating portrait of a particular world, with characters as believable as any real-life acquaintance. The Abomination is a terrific book by any standard; as a first novel it is outstanding.

After Sjöwall and Wahlöö came Henning Mankell, followed by a flood of Scandinavian mysteries, nearly every book scrupulously plotted and coldly realistic, individually original but en masse forming a recognisable subgroup in the crime fiction genre. The Hammer siblings have not broken away from the almost obligatory police-procedural; their hero is a Copenhagen cop with the familiar kind of team that includes its statutory women and the inevitable interfering politician. Nonetheless, their story is original. Five dead men have been found mutilated and hanged in a school gymnasium. It is soon clear that these men had all been serial sexual abusers of children, and the detectives find the press and public unwilling to provide information or help. A vigilante campaign, marches and manifestos ensue. Will or should the unidentified murderer get away with it? Was killing these monsters a crime or a public service? The Hanging is an unsettling, thought-provoking novel.

‘Do you know why there are no detective novels in Hebrew?’ Inspector Avraham Avraham asks. He gives the answer himself: ‘Because we don’t have serial killers; we don’t have kidnappings; and there aren’t many rapists out there.’ Believing that crimes in Israel are straightforward, with no real mystery, Avi is sure that Ofer Sharabi, a teenager reported missing by his mother, will turn up very soon. But the policeman is wrong. Soon there is a major hunt underway for Ofer. The police investigation is complicated by the bizarre interference of a schoolmaster neighbour who, for no particular reason, concocts and delivers letters purporting to come from Ofer; and Avi’s increasing guilt about not taking the first report seriously does not help. Mishani is an Israeli crime writer, editor and literary scholar, who specialises in the history of detective fiction, and this, the first in a projected series of novels, contains many hints of complications in Avraham’s professional and personal life, presumably to be expanded in future books. The Missing File is subtle, slow-moving and original – a welcome addition to the police procedural genre.

Most readers will have no idea whether this novel is an accurate portryal of post-Soviet spies in Putin’s Russia and in contemporary America. It certainly seems to be entirely plausible and since the author worked for 33 years as a clandestine operations officer in the CIA, maybe it really is. If so, nothing has changed since the days of the Cold War. The beautiful Russian heroine is trained as a seductress in order to spy; the handsome American hero is a master of spycraft, brave and just sufficiently insubordinate to maintain the reader’s interest. Sections alternate between the inner workings of the Kremlin in Moscow and the Agency in Washington, where cynical old men send idealistic young operatives out to lie and die for their countries. Whether or not Red Sparrow is based on fact, it’s convincing and exciting.

Beth has spent ten years mourning and searching for her daughter Amy who, when ten years old, disappeared without a trace from the local playground. Then one day a stranger called Libby comes to Beth’s door, claiming that she knows what happened to Amy. Libby has a daughter, now aged ten, who is the spitting image of Amy and knows things that only Amy could have known. Must Beth and Libby conclude that reincarnation is possible? What other explanation could there be? This is the point at which I nearly put the book down, since in this column I don’t review tales of the supernatural. Luckily I persevered to the end of what turned out to be a gripping and well-written tale with a perfectly down-to-earth solution.

It was disconcerting to start Close My Eyes immediately after R S Pateman’s tale of a lost daughter. Here is another Beth – a stillborn baby – and another mother still obsessed by her loss years later. Here is another stranger on the doorstep claiming that the child is alive. Luckily the story works out very differently, leading to a quite melodramatic conclusion. This is the first novel for adults by Sophie McKenzie, an award-winning writer of children’s books. I found it readable but not quite credible.