Merce Cunningham, the beaming Yoda of modern dance, took a curtain call from his wheelchair at the Barbican, declaring this year’s Dance Umbrella festival open with an ear-stretching smile. Now almost 90, the American choreographer often seems serenely oblivious to anything other than what he needs for dance (famously, he only puts music and design in place after the choreography), but the outside world has a way of filtering through, and two pieces from this London visit, created almost 50 years apart, crackle with the energy of their times.

Crises looks brilliantly weird today, so I can’t imagine how strange it would have seemed in 1960. In red and yellowleo-tards by Robert Rauschenberg, it’s a pop-art cartoon for the atomic age. Dancers make paranoid scuttles round the edge of the stage, or frantic, jittery solo runs. To Conlon Nancarrow’s deconstructed honky-tonk piano, they revolve like satellites, angled on one foot. One woman even wibbles her hand like a cartoon death ray.

In a week when the global economy went into freefall, Cunningham’s most recent piece also felt pretty much on the nail. The backdrop for Xover (“crossover”) - also by Rauschenberg, who died in May - is a silkscreen collage of urban detritus (a bike, fence, sections of barriers) splashed on a white background. The score is a bonkers assemblage of John Cage, fragments of sound and live vocals (delivered by Joan La Barbara, swathed in robes, like a dippy priestess), flickering like outtakes from a lost radio station. La Barbara growls, purrs, sneezes and is at times quite literally barking.

Against this random assault, the dancers in white Lycra seem fragile figures, crossing the stage as if trying to locate points of stability. A central duet explores skewed balances, the partners leaning away as far from each other as they can until he scoops her up in his arms and carries her away from all this. The others remain, nervously watching the skies.

Cunningham’s dancers have a scrubbed, wholesome look. Spinning on uncertain ground, they’re open to anything, an attitude worth cultivating. Christopher Wheeldon’s performers in the second season for his company Morphoses are pure thoroughbred: sleek stars from New York City Ballet and the Royal Ballet. By all accounts, Morphoses had a muted start last year, but its latest Sadler’s Wells season, including two premieres and some smart revivals, felt like an event. It’s an abstract repertoire delivered without ceremony - Wheeldon himself made modest introductions from the stage each night.

Morphoses achieves luxury on a shoestring. The cast, he told us, had transported backdrop and costumes in their own luggage, like an old-fashioned touring party. His buoyant new work, Commedia, takes that energy. Set to Stravinsky’s Pulcinella – a series of bright, pointed numbers - it suggests a company fetching up somewhere and putting on a show. It skews nicely between commedia dell’arte - tumbling, Pierrots, Columbines - and back-stage relationships. Leanne Benjamin has a fizzy duet with Beatriz Stix-Brunell, 15, and a wonderfully warm one with Edward Watson. With delicious, crunchy detail, the piece is as nice as biscuits.

Wheeldon is perhaps dance’s most devoted classicist and its soppiest romantic. You could see both aspects in his teeming contemporary classic Polyphonia and in last year’s Fools’ Paradise, in which dancers swoon across a starry firmament to a plush score by Joby Talbot. The title suggests love - or at least the sumptuous delusion of putting yourself in another’s hands. Wheeldon lets Wendy Whelan, NYCB’s steeliest ballerina, be vulnerable. When lifted, she kinks her knees as if craving to be secured. Entrancing, even if it makes you wonder whether feminism actually happened.

Also on show were relative rarities: Ashton’s Monotones II and Six Fold Illuminate, to a grand, relentless Steve Reich score. The choreographer, Emily Molnar, throws everything at it in an attempt to make an impact on the music’s intractable rush. There’s a pyrotechnic solo for Watson, but it becomes exhausting to watch.

As Wheeldon may find, it’s tough to maintain a company’s spark. Though Rambert has ardent dancers, it is working a mediocre repertoire. Opening the autumn tour at the Lowry, Salfod, its artistic director, Mark Baldwin, unveiled Eternal Light, set to a new choral work by Howard Goodall. It’s a droopy Requiem for a world of waning faith. Sung by local choirs at each venue, its sorrow is also for the living, largely unsustained by belief. It’s elegiac and occasionally a bit Vicar of Dibley.

A choreographer of winning fluidity, Baldwin could perhaps use a more abrasive score. His vocabulary is airy - arms glide upwards, dancers rise onto toes, throwing out delicate shoots of optimism. It can feel lovely, but rarely achieves much purchase. The earnestness is enlivened by startling misjudgments. Ranks of floating crucifixes are outlined in Swarovski crystals (when belief falters, bling steps in). And Baldwin’s emblem of an imperilled natural world is a toucan. It’s a peculiar pick: the Carmen Miranda of the bird world isn’t designed to flutter limply. Toucans have vigour - what’s happened to Rambert’s?

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