BBC America "Broadchurch" on Netflix.

Crime dramas with a strong mystery at their heart seem perfect for the Netflix business model of getting viewers hooked on stories they can’t stop watching.

Gertrude Stein called mysteries the most demanding form of fiction, because a good mystery requires a watertight plot with believable events and logical characters. Anything less and the story falls apart. But a writer who pulls all this off creates a story that can’t be stopped until the finish.

Not surprisingly, the best version of this kind of story often comes from the land of Agatha Christie and Arthur Conan Doyle. Like many Americans, I seem to find an elevated joy in the British accent. And perhaps because Sherlock Holmes looms over the genre, something about British detectives solving these mysteries just seems right.

Also not surprisingly, Netflix seems to excel in this category. While it would take far too long to watch all of the streaming service’s offerings, the British crime shows featured below are a good start.

A special nod goes to “Midsomer Murders.” I didn’t highlight it below, as I can’t in good conscience tell you to watch 19 seasons of a show I haven’t watched myself, but Netflix’s description encapsulates both the darkness and the fun of these kinds of stories: “Ah, the idyllic English countryside. Flowers bloom, nightingales sing and homicide is as common as hay fever.”

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Streamline makes recommendations for streaming shows and movies. Every Saturday, Streamline highlights the best shows to watch online, with a focus on Netflix.

“Broadchurch”

BBC America "Broadchurch" on Netflix.

Premise: Two investigators team up in a beautiful coastal town called Broadchurch. Their first case together involves the murder of a young boy, the best friend of one of the investigators’ son. The death rips apart the community as fingers point between family and former friends.

Value: True acting talents, David Tennant and Olivia Colman, play the lead investigators, while Jodie Whittaker of “Doctor Who” plays the mother of the murdered boy. This coupled with the idyllic backdrop makes the show an easy watch, despite the grim subject. “Broadchurch” sets up a solid whodunit mystery with an answer that ultimately surprised me. Without revealing too much, I also appreciated that the show introduces the character that ends up being the killer in the first episode, making the mystery theoretically solvable by the viewer (even if I didn’t succeed in doing so).

Heads Up: “Broadchurch” doesn’t experiment much with the form. It sets out solely to be a solid crime drama, which by now is a well-worn genre. Success at this aim deserves praise, but I wish this show had more heft.

Trailer:

“Luther”

BBC "Luther" on Netflix.

Premise: A grizzled London detective pursues criminals who possess a particular moral bankruptcy, perhaps revealing something about his own character. He loses his wife’s passionate love while burying his head in the job and then has a hard time reckoning with not having everything he desires. In the first season, the detective goes after a brilliant murderer he can’t get off his mind.

Value: Idris Elba, who cemented his stardom with this role, succeeds in embodying the archetype of the angry, lovelorn detective who has seen too much. The camera follows the action with strange angles and movements, further adding to the vibe that the protagonist is never at ease. I particularly enjoy the work the show does to establish the character’s humanity amid the relentless hustle and rage. This detective can be oddly funny, and that’s important as he wades through hell.

Heads Up: The show has some pretty graphic shots of blood and guts. “Luther” wants to establish its unflinching intensity and tends to scream this through disgusting shots of dead bodies or by having Elba’s character literally scream at people. I found this show to be comically over the top at times.

Trailer:

“Collateral”

Liam Daniel/Netflix "Collateral" on Netflix.

Premise: London detectives try to solve the murder of a pizza delivery driver and find a complicated case with deep political implications. Drugs, illegal immigration and political corruption all affect their investigation. It also doesn’t help that the only witness wants to keep quiet for fear that any scrutiny into her life will reveal her affair with a female vicar.

Value: Carey Mulligan’s detective has the best background story ― she’s a former Olympian who had a viral pole vaulting accident. She’s also recently pregnant. When this detective shows more humanity to the suspects than her colleagues do, you can believe in her rebelliousness, because the show establishes her as someone who wants to be a champion and might just be one.

Heads Up: In its ambition, the plot gets a bit unwieldy. It’s simply unbelievable that so many big political implications would come from this one murder. That would be fine if the characters acknowledged this fact, but “Collateral” also establishes the central case as nothing that spectacular in the characters’ lives, so the ridiculous political coincidences become a narrative problem.

Trailer:

“Sherlock”

BBC "Sherlock" on Netflix.

Premise: A famous London detective teams up with a war veteran to solve cases that appear unsolvable. While tackling the one-offs, the detective also plays a cat-and-mouse game with a supervillain who appears to be his intellectual match. Whether the detective or the villain is one step ahead of the other is always anybody’s guess.

Value: Benedict Cumberbatch and Martin Freeman have become blockbuster stars since the start of this show, and it’s clear why. Both have a charisma that makes it hard not to root for their characters or even just to hang out with the duo in their shared apartment. Unlike more realistic crime shows, “Sherlock” has fun cases to solve that have a whimsy to them even when murder is involved. I’m also a sucker for stories that credibly establish a “brilliant” character and then have that character overcome various challenges.

Heads Up: The episodes have movie-length run times, but don’t always wrap up storylines and can’t compete in narrative quality with stand-alone movies, giving viewers little payoff. The seasons only have a few episodes, but I find the choice to truncate the stories this way to be disorienting.

Trailer:

“The Fall”

BBC "The Fall" on Netflix.

Premise: A female detective plays a cat-and-mouse game with a male serial killer who gets off on torturing and murdering young women. Working for the London Metropolitan Police, the detective goes to Northern Ireland to try and find the killer. This killer has a normal-seeming life as a husband, father and professional psychiatrist.

Value: If you have a thing for stories like “50 Shades of Grey” then you’re in luck, because Christian Grey himself, Jamie Dornan, plays the sexually motivated killer in this series. Gillian Anderson (“The X-Files”) plays the detective. The show tries hard to establish that even murderers are human, giving the killer a full life and backstory. As with any good cat-and-mouse narrative, “The Fall” shines in the numerous “close call” moments that make you think the killer is about to get caught, but then doesn’t.

Heads Up: Perhaps the initial aim here was to highlight the real and troubling problem of abuse against women, but the end product is a show full of titillating murders carried out by a young, attractive movie star and presented with novel camera pans. If stories of sexy murders are your thing, then this will probably do it for you ― critics have been favorable, and that’s why I’m highlighting it here. Otherwise, you may find the moral core of this show to be rotten. Yes, all of these crime shows make entertainment out of murder to some extent, but rather than use the murder as a source of great tragedy, this seems rooted more explicitly in perversion.

Trailer:

A few more to consider...

“Marcella”

A former London detective returns to work to investigate a serial killer after her husband leaves her. She experiences long blackouts and fears she might be the killer when the woman her husband had an affair with winds up murdered.

“Happy Valley”

A police sergeant in West Yorkshire still struggles with the suicide of her daughter and her divorce from her husband, as she raises her daughter’s son (conceived through rape) with her heroin-addicted sister. These terrible circumstances lead to a case the sergeant needs to solve for both her job and her personal well-being.

“River”

A London detective struggles with the murder of his partner. Fighting with his boss to keep his job despite his unraveling mind, the detective remains obsessed with finding the killer while struggling to solve new cases.

“Hinterland”

A detective gets tangled in a complicated case that takes place in a Welsh town. One murder may have implications that stretch generations.

Netflix has a particularly funny and ridiculous description of this show:

“Being a cop in London is murder. A village in Wales sounds like a good beat. But murder never takes a holiday.”

“Shetland”