EDINBURGH.- If you say “Edinburgh Festival” to most people, they’ll probably think of the Fringe. But the Fringe — primarily a showcase of up-and-coming acts from English-speaking countries — is actually an offshoot of the more global, highbrow and judiciously curated Edinburgh International Festival, and the two events run side-by-side.

The theater offerings in this year’s International Festival showcase the brightest Scottish talent alongside shows from around the world and fall into two categories: While the international plays are overtly political, encompassing disability rights, anti-racism and ecology, the homegrown works explored the more personal terrain of addiction, recovery and self-care.

One of the most eye-catching items on the bill was a metafictional spin on “Hamlet” by the Peruvian company Teatro La Plaza, which ran at the Royal Lyceum Theater Edinburgh this month. This production, performed by eight young actors with Down syndrome, charts the journey of a similar, but fictional, group as it prepares to put on a production of Shakespeare’s famous tragedy. The actors perform snatches of “Hamlet” — there’s a murdered father, a ghost, a play within a play — and try to connect its storyline to disability: Polonius’ protectiveness toward Ophelia, we are told, echoes society’s tendency to infantilize people with Down syndrome.

But there isn’t much thematic overlap, and this “Hamlet” is mainly a cipher for the power of storytelling. In a key scene, Álvaro (Álvaro Toledo) sees Jaime (Jaime Cruz) trying to replicate Laurence Olivier’s famous performance in the 1948 film adaptation, which plays on the screen behind him. Álvaro upbraids Jamie for trying to play the part “like a statue.” The message, that people with Down’s must carve out their own paths rather than assimilating to normative expectations, is later reiterated in a defiant punk rock routine.

The cast appears in casual rehearsal attire, but a dazzling selection of spotlights (by Jesús Reyes) injects a sense of magic. The actors are capable and immensely charismatic, and there are a number of funny moments including a fake Skype chat with Ian McKellen. But Chela De Ferrari’s script fades toward the end as the concept drowns out the story and the play lapses into a cloying mushiness that sits uneasily with its anti-condescension message.

Those averse to didactic theater might want to steer clear of “After the Silence,” a work by Brazilian writer-director Christiane Jatahy, at The Studio. This polemical performance piece uses the unsolved murder of a labor activist as the springboard for an inquiry into the history of dispossessed African-Brazilians in the Chapada Diamantina region of the Brazilian state of Bahia. Three women (played by Aduni Guedes, Juliana França and Gal Pereira) talk us through a series of video clips that play on the screen behind them: Some of these show archival documentary footage; others are fictional reels featuring the actors themselves, shot on location.

The sheer visual beauty of that setting, combined with the raw power of the characters’ rage, carries the piece up to a point and there are several impressive musical set pieces as the women find solace and catharsis in dance, ably assisted by percussionist Caju Bezerra.

But the lack of a narrative arc makes itself felt. At one point França pleads with the audience, “I don’t want you to think this is only about pain,” which feels like Jatahy’s elevator pitch to the festival’s curators. The show, she insists, is also about love. We’ll have to take her word for it.

The natural world also looms large in “The Outrun,” directed by Vicky Featherstone at the Church Hill Theater. Adapted from Amy Liptrot’s 2016 memoir, it tells the story of a woman from Orkney, an archipelago off the northeastern coast of Scotland, who moves to Edinburgh and becomes an alcoholic. She staggers from one disaster to the next, before eventually moving back to Orkney to detox and find solace in nature and wild swimming.

Isis Hainsworth gives an assured display in the lead role and Paul Brennen is understatedly sympathetic, taciturn but tender, as her reclusive father. But Stef Smith’s adaptation is a depthless affair. We skip through the phases of the protagonist’s life at a pace that precludes empathy, and the play has the feel of a recap.

The production’s lush sound and visuals are a major saving grace. A large screen at the rear of the stage displays a series of beautifully evocative backdrops. The images are taken from nature — feathers, bones, water, hexagonal dapples of sunlight, roiling waves — but have a strange, otherworldly quality that is further enhanced by gorgeous stage lighting. At certain significant moments, a chorus wanders onto the stage and stands stock still while chanting ominously. The combined effect is eerily transporting. (Set design is by Milla Clarke, lighting by Lizzie Powell.)

Back at the Lyceum, “The Fifth Step” explores similar terrain in a more character-focused style. Written and directed by Northern Irish dramatist David Ireland, this is a superb dark comedy about the complicated friendship between two recovering alcoholics. Luka (Jack Lowden) is initially in thrall to the older, avuncular James (Sean Gilder), who teaches him concepts like boundaries, the dangers of codependency and why an alcoholic should never set foot in a pub, even if it’s just for a soft drink. (“You don’t go to a brothel for a kiss, yeah?”)

Lowden plays Luka with a shaky, twitchy diffidence that gradually gives way to assertiveness, while Gilder’s James has an aura of world-weary wisdom that gradually dissipates to reveal a questionable character. The dialogue is a witty blend of emotional intensity and comic bathos, with sardonic gags about religion, relationships and sex, a hilarious plot twist and the occasional moment of surreal whimsy. The most conventional of the plays at this year’s festival is also the strongest by far: no screens, no gimmicks — just excellent theater.

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Edinburgh International Festival

Through Monday at various venues around Edinburgh; eif.co.uk.

This article originally appeared in The New York Times.