As Voldemort's delved deeper into Dark Magic, his appearance became more snake-like, while he acquired a more serpentine countenance. This most probably explains why he got a much flattened nose. The legendary Voldemort's serpentine appearance is made mention of in all books. According to theories, every murder Voldemort committed brought more distortion to his already distorted face. There was a particular scene where Dumbledore reminded Harry of Voldemort when he resurfaced from his ten years exile. He came to ask Dumbledore the newly appointed headmaster of the Defense Against The Dar Arts Position and hide the Ravenclaw Horcrux. His appearance changed quite drastically. It is believed that this happened ten years earlier when he worked with Borgin and Burkes around circa 1956. It won't be unfair to insinuate that Voldermort had something deep to do with Dark Magic; Dumbledore, however, hopes that half of everything he has heard about Voldermort Dark Magic involvement and secrets were lies.
Here is a super short answer with regards to the movies: CGI had Voldermort's nose removed. Voldermort's nose was extensively discussed in some segments in the extra scenes. Ralph Fiennes never agreed to the use of the flat nose, but he was persuaded with the argument that the flat nose gave the character a very scary visual appearance.