This ambitious identity-and-imperialism saga sees the American actor take on several different roles – and demands your full attention.

Robert Downey Jr really Robert Downey Jrs the hell out of The Sympathizer. He thunders around in a vast array of prosthetics, giving off that weird, intense aggro-magnetism, and it might be the sheer Robert Downey Jr-ness of him that explains why it took me until halfway through the second episode to realise that he wasn’t playing the same character in disguise, but several different characters, and that The Sympathizer is very much that kind of show. Still, given that it is an adaptation of Viet Thanh Nguyen’s Pulitzer prize-winning novel and has been directed by Park Chan-wook (Oldboy, The Handmaiden), it would have been foolish to turn up and expect its cerebral identity-and-imperialism saga to be handed to you in easily digestible chunks.

Naturally, it makes you work, demanding that you follow along as it peacocks and pirouettes around the plot and its themes, which is largely thrilling and occasionally a little wearying. The timeline jumps all over the place, but it begins roughly four days before, and four months after, the fall of Saigon. The anonymous Captain (Hoa Xuande) is a half-French, half-Vietnamese police chief and loyal enforcer of the Southern Vietnamese General (Toan Le), while also being mentored by CIA agent Claude (Downey Jr, in the first of his multiple roles), except that he is also, also, a spy for the Communist North, embedded deep in the regime that he opposes.

We know that not everything goes quite to plan as, later, the Captain is in prison, having been captured by his own side – his real side, not his fake side, though the boundaries do become increasingly blurred. In captivity, he is repeatedly told to report everything that has happened to him. As he writes it all down, again and again, details and memories and decisions shape-shift and are reinforced or remade. A draft is rejected for having a Hollywood ending. What story is he supposed to tell?

The unreliable narrator isn’t so much introduced as sprinkled all over the series with a flamboyant flourish. Early on, a scene is rewound and replayed, with Downey Jr delivering the same line in a slightly different register. Memory is unreliable, and we cannot fully trust what we are seeing. This is stuffed with stylistic tics and the visual flair you’d expect from a director who is known for it. Images repeat themselves, becoming bookmarks in memories. A man’s head turns into an egg wearing glasses, which foreshadows a gruesome death. Scenes are cut abruptly and aggressively between locations and time periods. You might not want to know what happens to the squid until you’re right there in the moment, hearing all about it.

It begins in Vietnam, where, before Saigon falls, we see the duality of the Captain’s life there, as he tracks and interrogates spies with whom he is also collaborating. After an off-the-books flight out, set up by the CIA in order to allow the General to flee the country, the action moves to Los Angeles, while darting back and forth and all over the place, in time and location. The old-fashioned spycraft provides lots of old-fashioned fun. There are miniature cameras, there’s invisible ink made from household items, a secret code used to send messages back home. There are elements of war, particularly in the harrowing escape from the airfields near Saigon, and this is all perked up with moments of wit and levity.

In the US, the Captain, who had been a postgraduate in the US 10 years earlier, returns to university and meets Sandra Oh’s Sofia, who rivals Downey Jr for big-star charisma, and with whom he has a steamy affair. It expands into postcolonial theory and academia, dips into a parodic take on an Apocalypse Now-style Hollywood blockbuster, and generally feels like big and ambitious storytelling that is able to balance its tonal lurches well. It is often darkly funny, often gravely serious, violent, emotional and even silly, and it poses grand questions and leaves them to linger, uncomfortably, without serving you the answers on a plate.

The only downside to all this is that, on occasion, it feels like it has blown all of its emotional budget on style rather than substance. There’s nothing inherently wrong with that – it’s a good-looking show, performed brilliantly, and it is fantastically ambitious – but sometimes that leaves it having to explain what’s happening with a poetic voiceover, rather than letting it play out seamlessly, for example. You can see this in the Robert Downey Jr conceit, which I admit I found distracting, as good as he is in the roles. For the most part, though, The Sympathizer is exciting, meaty and a reminder that drama that demands your full and complete attention can be well worth the effort.