The ongoing John Wick saga is a fairly simple story with a world of complexity hidden just behind its on-screen events. Though it's a very compelling narrative, it's always been influenced by a lot of different sources. A closer inspection, however, suggests that the iconic action franchise might have always been borrowing from much deeper lore.
Most popular modern material is based on something, either directly or through inspiration. Movies based on books, stories based on other stories, riffs on genres established generations ago, repeating themes, and story structures that never seem to die are all over the modern multiplex. Some stories are foundational, and their influence can be felt in everything.
In an interview with Variety, John Wick franchise director Chad Stahelski stated that he and his crew have always seen the eponymous assassin as an Odysseus figure. There are numerous other fictional characters to whom the Baba Yaga has been compared over the years, but, his creator sees him as the hero of Greek myth. There are certainly some similarities and references. The obvious one is Charon, the doorman and concierge at the Continental hotel who happens to be named after the ferryman of the river Styx. It does, however, seem strange that a character known for killing roughly a thousand people in pursuit of personal vengeance would be compared to the classic epic hero. The franchise is actually borrowing from far more than one classic Greek epic.
The first John Wick film, when boiled down to its essential elements, is about a man who gave up the life of a warrior being forced to take up his weapons once more. He spends most of his life at war and manages to give it up, only to be dragged back due to the death of a loved one. He destroys everyone who stands between himself and his enemy, he tangles with forces much more powerful than himself. When he's done, he finally earns a moment of peace. The tale is strikingly similar to the plot of The Iliad. The story before The Odyssey is a much more violent affair, telling the tale of war that lands Odysseus in the position he takes in the sequel. In this way, Wick is both Odysseus and Achilles. He finds peace, returns to war to avenge a loved one, and as the High Table comes into focus, the character shifts in many ways.
The journey of Odysseus really begins when he's cursed by the cyclops. His struggle against the sea full of monsters mirrors John's battle with a city full of assassins. John tangles with deific figures of power and importance. While, in the first film, he was an unstoppable rampaging super soldier, his role in the second film is often more transient. He's routinely at the whim of people who have connections that make them into domestic gods. The Bowery King, the lord of New York's homeless people, is the Athena figure. He's the only god who offers support, though in a limited fashion. He even lets John take the disguise of a beggar for a moment, just like Athena. Though his journey features many interesting parallels, John differs quite a bit in character from his supposed inspiration. Interestingly, this might make him more interesting as a cinematic reference.
Odysseus is the ur-example of a Greek epic hero. He perfectly fits the period and narrative structure of the genre. Though John Wick follows a similar story, he doesn't share a lot of traits with the ancient protagonist. They're both gifted warriors, lauded far and wide for their skill. Part of the draw of Odysseus is his mental acuity. He outsmarts his foes as often as he defeats them physically. John isn't the strategic type. He never really has to be, he just solves his problems through the superior application of violence. In addition, the downfall of Odysseus is his hubris. Wick's biggest weakness is his obsessive need to seek vengeance, which leads him to make enemies with almost everyone. Arguably, this is an elevation of the concept. Wick is both Odysseus and Achilles, combined and updated for the modern age.
The heroes of Greek antiquity formed the backbone of John Wick's legacy, but the character perfectly fits the story. Where The Iliad and The Odyssey are epic poems, John Wick is a neo-noir revenge movie. As such, a taciturn nature, a capacity for violence, and the continued self-destructive pursuit of self-serving vengeance become his default traits. The story may have been inspired by mythology, but the art was inspired by 40s noir and 80s revenge films. Perhaps the most interesting aspect of the franchise's mythology is the way it blends multiple concepts from wildly varied sources. John Wick fits the role ascribed to him by his creator, but he also perfectly fits the elevated action film he helped create.