In some Edinburgh Fringe seasons the Traverse Theatre’s programme is more overtly themed than in others. This year, no overall label is being flaunted, but as I spent my first day serially watching the offerings in the smaller Traverse 2 space, a number of common preoccupations seemed to emerge.

Craig Higginson’s The Girl In The Yellow Dress is an intriguing two-hander which repeatedly sets up expectations and then either swerves around them or keeps us hanging on right until the end. Celia is an Englishwoman in Paris who offers her services as an English language and conversation tutor; Pierre, who is of Congolese extraction, requests lessons from her. The power of the play is not simply its cleverness with narrative developments: is he all he seems? Is she? Will they get together? Will it work? Higginson shows us each protagonist creating their own persona and managing the other’s impressions and expectations by means of linguistic manipulation. Figures of speech and constructions are defined explicitly even as Celia and Pierre deploy them. Of course, we all use language in this way even at our most intimate. But it is unusual and fascinating to see a play investigate the extent to which words can shape our thoughts and feelings as much as vice versa.

Malcolm Purkey’s production (for the Market Theatre of Johannesburg, Live of Newcastle and the Glasgow Citizens) allows us to see this schematic structure without letting it crush the human interaction. Each act carries a title caption of some part of speech (The Passive, for instance, or The Conditional), as Marianne Oldham and Nat Ramabulana repeatedly engage with and disengage from each other. Oldham is particularly compelling, constantly wearing a smile that suggests there are volumes behind it… as indeed there are.

Linda Brogan and Polly Teale’s Speechless is based on Marjorie Wallace’s book about identical twins June and Jennifer Gibbons, who refused to speak to adults and communicated with each other in a private language; after torching their secondary school, they were committed to Broadmoor. In Teale and Brogan’s version, language is both a bond and a barrier. The outside world rejects them (Barbadian-born, they live in Haverfordwest), so they likewise reject it; yet, in the end, however much they – especially Jennifer – may yearn to be a single being, their words and silences differentiate them from each other as well as from everyone else. Natasha Gordon and in particular Demi Oyediran as June turn in a remarkable pair of central performances in Teale’s production. However, the Shared Experience company’s trademark of impressionistic physical performances reinforcing a text is no longer as distinctive as it once was, and especially in an Edinburgh context this theatrical area is as much a buyers’ market as any other.

While You Lie continues Sam Holcroft’s predilection for tackling complex knots of topics with often unpleasant results. It should be emphasised that in some cases “unpleasant” can be a compliment, and when I say that this is a deeply unpleasant play I mean it as high praise. Ana, an immigrant from eastern Europe, her boyfriend Edward, her office boss Chris and his wife Helen connect in a series of sexual and power relationships, symbolised by the passage from one to another of a pink shirt in a kind of sartorial La Ronde. Each has concerns about their image, both physical and psychological, and their sexual identity; each finds themself consulting cosmetologist Ike, who is attempting to raise sponsorship for a programme of cosmetic surgery to help women mutilated in war. Matters build to a climactic event which, though grotesque, is still less disturbing than the play’s message about the extent to which we will injure ourselves in order to win the approval of others. Zinnie Harris’s production is cool and unfussy, and true to Holcroft’s apparent intention that there should be little or nothing graphically portrayed which might give us the excuse of dismissing it as visually unpalatable rather than, as it is, conceptually unflinching.

After such a trio, D.C. Jackson’s My Romantic History is an immense relief. Thirtyish Tom recounts his relationship with co-worker Amy, interspersed with recollections of his past amours and in particular the undying echoes of his first teenage love; we then see the same relationship from Amy’s point of view, with her own personal chronicle and first boyfriend interwoven. It is staged by Lyndsey Turner with her characteristic flair and vitality, and Iain Robertson excels in making Tom appealing to the audience but far from unambiguously sympathetic. I hope it does not seem shallow to remark that matters begin to drag in the final phase when events take a serious turn.

The Traverse also continues its Festival habit of presenting shows beyond its own walls. Flesh And Blood & Fish And Fowl is in St Stephen’s, a space now sadly underused since the dormancy of the Aurora Nova venue there a couple of years ago. Geoff Sobelle and Charlotte Ford go jointly and severally through a series of near-wordless workplace scenes which start off absurd and grow ever more so, as the nondescript office set gradually transforms into a forest wilderness. It is an impressive work of staging and design, but I felt that at times the piece fell into the modern-jazz trap of riffing, not upon its main themes, but recursively upon its own riffs.

The Traverse also administers the tenth-anniversary return of site-specific specialists Grid Iron with Decky Does A Bronco, staged in the same park playground in the city where it was first seen in 2000. Not only does Douglas Maxwell’s play about the passing of a childhood spent on the park swings still resonate; it resonates doubly for those who saw it first time round, as a memory play becomes itself an event of recollection of past festivals, and that era’s goldenness is reflected in this one as evening shadows fall across George V Park.

Written for the Financial Times.