Expectations can be dangerous when it comes to live music, but sometimes managing them is easier said than done. Go and see a band like Jaga Jazzist, a genre-crossing collective of Norwegian multi-instrumentalists who skyrocketed to fame in 2002 when the BBC named A Livingroom Hush jazz album of the year, and you expect it to be big. Especially when it’s the group’s 20th anniversary tour and you arrive at Union Chapel to find the queue stretching around the block.

Various Artists: Native North America (Vol. 1) – Aboriginal Folk, Rock and Country 1966–1985

There is an odd moment about halfway through Lily Allen’s set. Clad in a shaggy white mini dress akin to a Puli dog’s coat, she announces the next song will divide the audience into those that love it and those that hate it. Her sweet voice then wraps itself around the soundtrack to last year’s John Lewis seasonal TV ad, her version of Keane’s “Somewhere Only We Know”.

Last night Latin jazzers J-Sonics confirmed their reputation as one of the most compelling proponents of the delicate art of fusion with a deeply grooving, deeply addictive performance of their propulsive repertoire. Their two Brazilian-flavoured sets were characterised by supple instrumental interplay, including from the singer Grace Rodson, a regular performer with the Roberto Pla Ensemble, whose taut, rippling vocalising rhythms and sumptuous tone were as crucial within the band’s instrumental textures as her solos, which smouldered, then burst into hot Latin fire.

It has become a staunch tradition that Kasabian gigs end with their fourth single, 2004’s “L.S.F. (Lost Souls Forever)”. By the time they reach it, a good chunk of the Brighton Centre’s capacity crowd, encouraged by guitarist Serge Pizzorno, have clambered on the shoulders of an associate.

Until recently, The National were a band for the knowing connoisseur, best known for their wry wit and tasteful guitar sheen. They seemed too niche for the O2 Arena, where they played their biggest ever UK headline last night. But that big tent of consumerism has now claimed them, and before an appreciative but rather lukewarm audience, somehow they seemed a little more ordinary and mainstream.

It’s not easy to write about a gig when you’re still shaking with adrenaline, still less so when that gig is the grand finale of the 2014 EFG London Jazz Festival, the climax to a giddy ten days of world-class contemporary music. But it’s a cross I’ll have to bear, because last night’s performance from legendary saxophonist Charles Lloyd and jazz giants tenorist Joe Lovano and trumpeter Dave Douglas demands it.

Imaginatively constructed and endlessly surprising, this world premiere of the complete version of pianist Robert Mitchell's choral work Invocation elicited one of the most moving performances I had the pleasure of hearing at this year's EFG London Jazz Festival. Written as “a personal and universal thank you to life-changing teachers”, the vast, six-movement work skilfully interweaved the improvised with the composed, resulting in a score of quite astonishing richness and variety.

Kassé Mady Diabaté is one of the great singers of West Africa, a member of Toumani Diabaté's Symmetric Orchestra and, more recently, the Afrocubism all-star line-up. His latest album Kiriké (Horse’s Saddle) on the Parisian No Format label is a beautiful return to his acoustic, traditional roots as a singer, produced by French cellist Vincent Segal and featuring kora maestro Ballaké Sissoko, Lansiné Kouyaté on balafon and Makan Tounkara on ngoni, conjuring up the spirits and messages of centuries-old Bambara songs of the ancient Manding Empire. This music runs deep.

Paying homage to the legendary imprint that brought us 'The Finest In Jazz Since 1939', this concert on the penultimate evening of the EFG London Jazz Festival really did have everything, including the unlikely sight of master pianist Robert Glasper pirouetting across the Royal Festival Hall stage. The first half saw Glasper in duo with fellow NYC-based Houstonian, pianist Jason Moran, in an extraordinary, hour-long set that referenced jazz past, present and future.