In an interview with Screen Rant, the directors of Avengers: Infinity War discussed how the relationship between Tony Stark/Iron Man and Peter Parker/Spider-Man continues to evolve during the film.
“And [Tony] still has this connection with Spider-Man that he’s established, and that evolves,” said Anthony Russo, who is co-directing the film with his brother, Joe. “And they basically have a unique mentor-mentee relationship that continues to evolve as they move into this film.”
Iron Man was the first superhero in the Marvel Cinematic Universe, but Spider-Man was a late arrival, only premiering in Phase 3. After a brief cameo semi-drafted to help Tony in Captain America: Civil War, Peter went on to star in his own film, Spider-Man: Homecoming, with Tony as a major supporting character.
That movie made Tony into Peter’s mentor, trying to protect him while assuaging his own guilt for his actions in the previous episode. In some ways they even had a father/son dynamic, which also occurred in the original Civil War comic, albeit with a less friendly ending for the two.
In addition, in the MCU Tony provided Peter with his spider-suit, as opposed to him making it himself as in the comics; it has all sorts of nifty new abilities as a result. It has been confirmed that Avengers: Infinity War will have Spider-Man don the Iron Spider suit, which some believe is could set up Tony’s final retirement from heroics at the end of Phase 3.
It remains to be seen exactly what will happen between Tony and Peter, and really, between Tony and all of his fellow superheroes; many are still angry at him for his actions in Captain America: Civil War.