This has been an excellent Cannes, despite a middling opener from Jim Jarmusch – a tongue-in-cheek zombie comedy called The Dead Don’t Die, which was moderately amusing when we were hoping for immoderately.

It is not merely that great work has been presented by the established old-stagers and silverback gorillas of the festival’s history; there has been great work from newer names and younger voices, too. There were outstanding films by Pedro Almodóvar, Ken Loach and Quentin Tarantino, each of whom delivered thoroughly characteristic work, but deeply satisfying for all that. Almodóvar’s Pain and Glory is a complex, absorbing auto-fiction based on the director’s own life. Ken Loach’s Sorry We Missed You, with its well-researched screenplay by Paul Laverty, is an angrily passionate denunciation of zero-hours Britain. And Quentin Tarantino gave us a showstopper with his extraordinary late-60s LA exploitation thriller Once Upon a Time … in Hollywood, starring Brad Pitt and Leonardo DiCaprio. Cannes’ youngest master, that remarkable 30-year-old veteran Xavier Dolan, had me utterly romanced with his complex love story Matthias & Maxime.

Korean directors and Korean films are always treated with great respect at Cannes, even if they don’t usually get the awards. That could change with Bong Joon-ho’s excellent suspense drama Parasite, a movie like Joseph Losey’s The Servant, about a young man from a poor family welcomed into a rich household as an after-school tutor for their teenage daughter.

But the film that everyone has been talking about the most, and which I am tipping for the Palme d’Or – of which, more in a moment – is Céline Sciamma’s Portrait of a Lady on Fire, an impossibly gorgeous, suspenseful and sexy-cerebral movie about an 18th-century French noblewoman (Adèle Haenel) who is painted in secret by an artist (Noémie Merlant) employed by her mother. It is Hitchcockian in its elegance, but shot and framed with classical restraint.

Another film that has swept people away here is Mati Diop’s wonderful Atlantique, which is about migrants and boat people, with an unexpected but utterly confident and plausible dimension of the supernatural. What a wonderful Cannes debut for Diop.

Elsewhere, the Brazilian director Kleber Mendonça Filho, in collaboration with his former production designer Juliano Dornelles, gave us an extraordinary and very mad thriller entitled Bacurau, clearly a satire inspired by Jair Bolsonaro and the far right. It is a very good film, although I suspect it isn’t quite winning people’s hearts here as much as Filho’s earlier, more gentle and ruminative pictures. Ladj Ly’s Les Misérables is a fierce social-realist drama-thriller about race and class tensions in the Paris suburbs, and it has been much talked about here, although I thought it becomes a bit derivative once the violence kicks off, and is rather better at depicting day-to-day normality. The Romanian director Corneliu Porumboiu reaffirmed his reputation for offbeat comedy with The Whistlers, about criminals secretly communicating in the “whistling” language of La Gomera in the Canary Islands.

Among the films that disappointed me, just a little, I have to include Terrence Malick’s A Hidden Life, based on the true story of Franz Jägerstetter, an Austrian conscientious objector and anti-Nazi protester during the second world war. It is a work of great moral seriousness and yet the whispery-plangent mannerisms are unchanging, and this man’s spiritual crisis did not look obviously different from Christian Bale’s agonising screenwriter in Malick’s Knight of Cups. Marco Bellocchio’s The Traitor, about the Sicilian mafia maxi-trial of the 1980s, is strong but perhaps not always inspired. The Dardennes brothers’ Young Ahmed has a weak, unsubtle ending.

And Abdellatif Kechiche’s Mektoub My Love: Intermezzo is an insanely overlong visit to a nightclub, in real time. It seems to have no point other than to ogle semi-naked and naked women.

But what a thrilling, exhilarating, exhausting Cannes it has been. Here, as ever, are my awards predictions, and I have also offered imaginary prizes in categories that the Cannes jury does not address: cinematography, production design, music, best supporting actor and actress.

Peter Bradshaw’s prize predictions

Palme d’Or: Portrait of a Lady on Fire (dir Céline Sciamma)

Grand Prix: Parasite (dir Bong Joon-ho)

Jury prize: Atlantique (dir Mati Diop)

Best director: Quentin Tarantino for Once Upon a Time … in Hollywood

Best screenplay: Xavier Dolan for Matthias & Maxime

Best actor: Antonio Banderas for Pain and Glory

Best actress: Debbie Honeywood for Sorry We Missed You

‘Imaginary’ Cannes awards – AKA Braddies d’Or

Best supporting actor: Alexis Manenti for Les Misérables

Best supporting actress: Sônia Braga for Bacurau

Best cinematography: Dong Jingsong for The Wild Goose Lake (dir Diao Yinan)

Best music: Once Upon a Time … in Hollywood

Best production design: Andrea Castorina and Jutta Freyer for The Traitor (dir Marco Bellocchio)