Billie Eilish may be one of the biggest names in new music, but here at the O2 Arena, she’s just Billie – the one who stares deep into your soul, smiles at you like she knows your secrets, and shouts “I love you” like she means it. “You are seen, you are safe,” she tells us. We believe her. And judging by the thousands of utterly hysterical fans, heaving and shaking with sobs amidst their singing – mostly clad in jorts, sports vests and ties – the feeling is mutual.

The O2 has to be the K2 of comedy peaks: a vast ovoid drum of a place where those right at the back have to be content with watching magnified images on screens. And for a standup, there are no electric instruments to drown out the echoing acoustics.

Exactly 40 years since Madonna’s first UK hit, “Holiday”, was skittering about the Top Five, she launches her global Celebration Tour at the O2.

In 2017, Bolton comic Peter Kay had to cancel his planned tour because of “family circumstances”. But then, when he announced last year that he was back in the saddle, the tickets for Better Late Than Never sold like the proverbial. Well into what has mushroomed into a mega tour continuing until 2025, I caught him at the O2 Arena.

Born in the bedroom of keyboard player Charles de Boisseguin, bathed in a sleek, quintessentially French tradition of electro-pop, L’Impératrice materialised on the darkened stage at the O2 Shepherds Bush, with glowing hearts beating in unison on their chests. The beat quickened into a single tone to lead into “Off to the Side”, leaping from an intimate, near whispered opening to a snappy, electric chorus.

The lengthy ovation Chris and Rosie Ramsey received when they walked on stage at the O2 showed there was a lot of love in the room, and why wouldn't there be? The married couple's podcast Shagged. Married. Annoyed. has clocked up 144 episodes and built a large and loyal following, and now here they were doing the show live.

I can’t look at Rod Stewart without thinking of Barbara, one of the naughtier girls in my third-form class at East Barnet Senior High School. She was tiny, and obsessed with him, her hair cut like his. “Maggie May” was number one, playing from tinny trannies in lunchbreak. It was from Every Picture Tells a Story, the album that established Stewart’s solo career. Barbara was in seventh heaven.

Abba fans can already have an immersive dining/dancing/singing experience at the O2 in Mamma Mia! The Party, and now, almost as a companion piece, is ABBA: Super Troupers The Exhibition, a show that sets out tell “the story of the band, their music and the era they defined”.

That's a pretty tall order and I'm not sure – even as a dedicated fan – that Abba defined an era, but on the other two points this multimedia exhibition makes a decent go of it as it describes the group's history from first meeting to eventual break-up, and beyond.

The O2 is usually a bright, sterile space before the bands come on. Its starkly lit US sports event ambience is accentuated by humanity milling around layered plastic seating clutching giant tubs of soft drink. Not so tonight. The venue has been open for three hours before the headline act is due. The lighting is purposefully dingy as 2ManyDJs and James Holroyd spin techno-flavoured sounds, warming up the crowd.

Jack Whitehall is hardly ever off the telly, appearing on gameshows or jollying around with his father, Michael, presenting the BRIT Awards and proving to be a decent actor in dramas such as Decline and Fall. But now he's gone back to live comedy with his new show Stood Up.