The discerning streaming service for those overwhelmed by the mass of content on Netflix and its ilk, Mubi offers a curated, rotating selection – one in, one out, every day – of 30 classic and contemporary arthouse films, with an array of themed seasons and mini-retrospectives dedicated to certain film-makers or movements. While its remit is global, European cinema obviously features heavily. On the menu at time of writing: Greek film-maker Babis Makridis’s vicious, Sundance-acclaimed black comedy Pity; Wim Wenders’ early existential thriller The Goalie’s Anxiety at the Penalty Kick; and the little-seen Ingmar Bergman chamber piece Crisis. A subscription is £7.99 a month; in the Rentals section, non-subscribers can access more than 150 pay-per-view films – from Jean-Luc Godard to Portuguese post-modernist Miguel Gomes – for £3.49 a go.

Yannis Drakopoulos in Babis Makridis’s 2018 Sundance-acclaimed black comedy Pity, available on Mubi. Photograph: Collection Christophel/Alamy

You’d expect a strong selection of classic and world cinema from the British Film Institute, and its attractively designed streaming service delivers – retaining the diverse, academic-but-accessible programming spirit of its cinema venues and DVD collection. It is obviously the go-to platform for British cinema history, showcasing its extensive archive – including shorts, newsreels and assorted curios – for free. Elsewhere, the film selection is rich on canon titles: the Italian Classics section includes works by Fellini, Pasolini, Antonioni, Rossellini et al, while Euro auteurs such as Éric Rohmer and Rainer Werner Fassbinder have their own dedicated collections. A running strand, selected and introduced by the Observer’s Mark Kermode, covers classics like Carl Theodor Dreyer’s Ordet and modern beauties such as Andrey Zvyagintsev’s Elena. Subscriptions are £4.99 a month.

Brigitte Federspiel in Carl Theodor Dreyer’s 1955 classic Ordet, available on BFI Player. Photograph: Everett Collection Inc/Alamy

As befits the UK’s leading arthouse cinema chain, Curzon Artificial Eye’s home streaming service is a classy affair, balancing a smallish back catalogue with a range of current cinema releases simultaneously available to view at home – a godsend to discerning film-goers who live outside metropolitan areas. French director Catherine Corsini’s heart-walloping melodrama An Impossible Love and Lars von Trier’s polarising The House That Jack Built are currently on that menu for £10 and £12, respectively. The library of older releases is indexed by actor, director, genre and country: France, for example, brings up an old-new Agnès Varda double-feature of Cléo From 5 to 7 and Faces Places – the former just £3 to rent. It is not a subscription service, and pay-per-view prices vary but members get a discount and exclusive free access to Curzon 12, a rotating dozen films currently including the Dardenne Brothers’ Rosetta and Deniz Gamze Ergüven’s Mustang.

Corinne Marchand in Agnès Varda’s 1962 masterpiece Cléo From 5 to 7, available on Curzon Home Cinema. Photograph: Moviestore Collection Ltd/Alamy

The monolith it’s impossible to avoid when having any streaming-related conversation, Netflix may be thought of as a largely American entertainment factory, but surprises are to be found in its International Films section. There, nestled among more popular European arthouse hits (Ruben Östlund’s The Square, Paul Verhoeven’s Elle), are the fruits of the streaming giant’s recent film festival buying sprees, rebranded and distributed as “Netflix Originals”. Seek out Sunday’s Illness, for example: a terribly titled but heart-grasping mother-daughter melodrama from Spanish director Ramon Salazar with Almodóvar allusions. (If you want the original article, Almodóvar’s Julieta is there too.) Older European fare is sorely lacking. Subscriptions start at £5.99 a month.

Isabelle Huppert in Paul Verhoeven’s 2016 arthouse hit Elle, available on Netflix. Photograph: Allstar

Amazon’s sprawling viewing options intersect with some of the above: Mubi and the BFI Player are in its network of add-on video channels, albeit with messier presentation than the standalone sites. But in terms of what’s available free, European cinema is speckled throughout: the organisation is a bit haphazard (you’re generally best off clicking the “International” header and seeing what comes up), but the gems are there. Titles range from crossover fare (Audrey Tautou in Coco Before Chanel, or Sweden’s saccharine Oscar nominee A Man Called Ove) to pleasantly surprising finds: Czech surrealist Jan Švankmajer’s morbidly brilliant mixed-media comedy Little Otik is lurking in the depths. Subscriptions are £7.99 a month.

Audrey Tautou in Anne Fontaine’s 2009 crossover film Coco Before Chanel, available on Amazon Prime. Photograph: Allstar

More of a niche proposition, Festival Scope is a two-tiered service, the most comprehensive of which is exclusive to film industry professionals and journalists; the public section is smaller, but deserves to be better known. There, international festivals offer web access to films concurrent with the festival itself: Venice, Locarno, Rotterdam and the Cannes Directors’ Fortnight are among the majors to take part. A limited number of virtual “tickets” to each film are granted – usually free – on a first come, first serve basis. A degree of vigilance is required, as is a willingness to take a chance on untested films. In the Films section, various undistributed festival picks are available for free: among them are Home, an impressively raw Flemish teen study, and Barrage, a low-key family drama from Luxembourg, starring Isabelle Huppert and real-life daughter Lolita Chammah.

Themis Pauwels and Lolita Chammah in Laura Schroeder’s 2017 film Barrage, available on Festival Scope. Photograph: Red Lion Films