Kallentoft’s books have been called beautiful, exquisite and original. I can see why: he writes in lengthy, almost poetic detail about Sweden’s landscape, townscape and record-breaking heat waves (or, as in his previous book, Midwinter Sacrifice, cold snaps), and he enters into the minds and motives of some of his characters. But he also has victims speaking from beyond the grave, their spirits lingering as the police investigate their deaths. The brutalised bodies of female victims turn up regularly in Summertime Death, though I can’t complain of tasteless or gloating descriptions, while the female police inspector who leads the investigation is an intriguing and credible character. Many people will admire this book greatly, adding to the huge success Kallentoft has had with previous books in the series. The supernatural interludes left me cold and irritated, so I found it good only in parts.

Another enormously successful Swedish import, Larsson is a remarkably good writer who has been well served by her translator. This novel was published in Sweden in 2006, her later books in the series having already appeared in English translation. Our heroine, lawyer Rebecka Martinsson, is single and has no children, her circumstances contrasting with the police detective Anna-Maria Mella, whose life and work are greatly complicated by her stroppy teenage daughter. In one of Larsson’s later books, Sweden suffers in an unimaginable heatwave. Here it is winter as cold as it can get, which in northern Sweden is very cold indeed. The body of a woman is found in a frozen lake, and prompts an investigation that leads to unexpected places and conclusions, uncovering corruption in one of Sweden’s richest corporations and crimes from the past that still cast dark shadows on contemporary events.

The Chicago private eye, V I Warshawski, is gently ageing along with her readers and her creator, but she still leaps into danger first and doubts her own good sense later. The other details of her life also continue unchanged: we meet again her elderly landlady and friend, the émigré doctor who serves as mother figure, and a collection of other recurring characters who are dislikeable but useful. One is her ex-husband, a lawyer who has gone over to the ‘dark side’ – that is, the establishment; others are various friends and acquaintances who all are willing to get into trouble, if not danger, to help Vic out. The case again concerns rich and corrupt members of the Chicago ruling class, all extreme Republicans, opposed as always to the much more sympathetic little guys. Of course Vic comes out on top in the end, but at a high cost to herself. And the book has a feeling of disappointment, of a lifelong liberal’s wasted effort, about it. ‘We not only hadn’t cleaned up the city, we hadn’t even made a dent. Instead, fraud had spread along every corridor of American life.’

In his long-running series featuring the police detective Roy Grace, Peter James has, up until now, shown his readers the seedy side of Brighton. This episode reveals the inner workings of the Royal Pavilion. James makes his fiction almost factual: he spends one day every week with the Sussex police in order to keep up with forensic developments, and he prepared to write this book by exploring the complicated network of tunnels and passages not usually seen by visitors to George IV’s extravagant folly. The plot involves a Madonna-style star arriving in Brighton to make a film about the king’s mistress, Maria FitzHerbert. Inevitably the star is besieged by devoted fans and deluded enemies, and it is Grace’s task to protect her. At the same time, his overlapping obligations include keeping his pregnant girlfriend safe from his own enemies, and overseeing the routine work of a busy CID. A complicated story straightforwardly narrated in this very superior police procedural.

I decided a while ago to stop reading or reviewing books that feature brutalised, tortured and murdered young women. But Criminal was described as a new departure for Karin Slaughter, a successful author of violent fiction. The story switches between the present day, when women are in command, and the 1970s, when Police Chief Amanda Wagner was a rookie, and female and black cops had to confront their white, male colleagues’ derisive hostility. It also switches between the bourgeoisie of Atlanta and its underworld, in which heroin-addicted young prostitutes live in avid, wretched squalor. Nobody cares, and almost nobody notices, when the girls disappear – that is, except for the heroes of this series of books, who do care and do investigate. The dyslexic detective Will, his lover, a widowed medic, and his boss Amanda, all find that their own lives are bound up with the fate of the lost girls. The plot is original and gripping, the style taut and vivid, and the tortures are not excessively dwelt on – but they are ingeniously, sadistically appalling and all the victims are, once again, pretty young women. I can see the merit of Slaughter’s writing and am sure that her fans will love this book. All it does for me is inspire nightmares.

This is the first in what is projected to be a series covering the years from the Queen’s coronation to the Prince of Wales’s wedding. The hero is a youngish clergyman, Canon Sidney Chambers, recently appointed as vicar of Grantchester, near Cambridge. In the Fifties, Cambridge is still a city of men, with only two women’s colleges, and clergymen still expect their parishioners to go to church. There are three mysteries in this volume: the suspicious suicide of a local worthy, the death of a young woman, and a case of art forgery. Sidney makes short work of them all, helped by his friendship with the local police inspector and by the energy of a glamorous neighbour. Life in a vicarage is something James Runcie, the son of a former Archbishop of Canterbury, inevitably knows intimately, and here he describes it exactly. But the book is an oddity with its deadpan narrative style and occasional interjection of prayer or theology. It’s a period piece that is a cross between a sedate story by Barbara Pym and one of Alexander McCall Smith’s non-violent morality tales.

A debut, due to be the first of a series featuring Alice Quentin, a psychologist whose problems include a schizophrenic brother, a personal history of abuse from her father, and such severe claustrophobia that she has to climb the stairs to the top floor of the tower block where she works. Under police protection, walking wounded after being attacked by a criminal who is at the top of the wanted list, Alice continues to work throughout all vicissitudes, using her special skills and insight in the hunt for a serial murderer of young girls. At the same time her love life is complicated, and soon becomes relevant to the case she’s working on. This good, gritty tale gives a detailed, depressing portrait of one kind of life in Britain in 2012. It’s the kind of book that future historians could use as evidence.

The latest instalment of this enjoyable series set in Iceland. A likeable American-Icelandic cop, a backdrop of ancient history, the country’s economic plight and the modern meteorological dramas all add depth to a compelling story.

Sensitive, vivid descriptions of daily life in Saudi Arabia combine with neat plotting in Zoe Ferraris’s excellent third novel. More please.