“In jazz music you have the freedom, you have the expression. You have the visceral and you have the intellectual. Everything can be expressed through jazz, and is expressed through jazz and through the medium of improvisation. This is the highest form of being able to create music.” Speaking at the opening press conference of this year's Copenhagen Jazz Festival, that definition of jazz from the 80-year-old saxophone colossus Sonny Rollins seems as self-contained and eloquent as any other I've heard.

Bassist, vocalist and composer, Esperanza Spalding is one of the most exciting things to happen to jazz in recent memory. Born and raised on what she has called “the other side of the tracks” in Portland, Oregon, Spalding grew up in a single-parent home. Encouraged by her mother, she began playing violin at the age of five and gained a place in the Chamber Music Society of Oregon. By the time she left, 10 years later, she had risen to the position of concertmaster.

A jazz concept album exploring the historical origins of Europe. No, not the synopsis of a new Christopher Guest film – although how I'd love to see Fred Willard in that - but an ambitious, far-reaching new recording from sax maestro Courtney Pine. Except, Courtney doesn't play any sax at all.

A recent Grammy nominee for his 2009 album Historicity, composer-pianist Vijay Iyer is one of an increasing number of young jazz artists who refuses to be corralled by genre. Iyer's work traverses a continuum that embraces everything from hip hop to orchestral music. Tirtha, his latest project, sees three great traditions seamlessly flowing into one another to create something vital and entirely personal.

Avant-garde art, by its very nature, always treads a fine line between the sublime and the ridiculous, and between entertainment and alienation. Thankfully this is something understood very well by the joint curators of Friday night's show at the Vortex Jazz Club: Baron Mordant of the Mordant Music record label and Jonny Mugwump of the Exotic Pylon website and radio show. As the names perhaps suggest, these are people versed in the potential deep silliness of what they do, even as they take it very seriously indeed – and their event certainly ranged far and wide between the weird, the wonderful and the out-and-out wrong.

Club music has always been hard to keep track of, and never more so than in the current climate of constant genre meltdown and cross-fertilisation. Which is why the DJ's art is more important than ever, particularly in the case of scene figureheads like the indefatigable Gilles Peterson – known for over 20 years as a patron of all things jazzy, but lately proving brilliantly adept at reaching all corners of what he refers to as “left-field dance music”. Shows like his are ideal – necessary, even – for nurturing, contextualising and showcasing new generation genre-agnostic talents like men of the moment James Blake and Flying Lotus who played at Peterson's Worldwide Awards on Saturday night.

There’s an interesting back story to The Trip. Before Rob Brydon was “discovered” by Steve Coogan’s Baby Cow production company in 2000, he was a workaday comic and Coogan was then at the height of his Alan Partridge-induced success.

It’s an interesting concept that Adam Hills has come up with for his latest show, Mess Around. The ever-smiling and hugely likeable Australian - a longtime sellout hit at the Edinburgh Fringe but who has yet to make a broader breakthrough like his peers - is a past master of audience interaction, so why not ditch the material and make that the show?

It takes a very talented comic indeed to warm the main room at the Leicester Square Theatre, a venue that is situated beneath a Catholic church and which, vampire-like, can suck the life out of even the most buoyant of audiences. Fortunately, Jason Byrne has enough energy to wake the dead or, in this case, a few hundred damp souls who have come in from a rainy London town outside.