He appears in the book and movie versions of 2010: Odyssey Two which is part of the Space Odyssey series. There, he is the American engineer who designed Discovery and was helping to build Discovery II to go back to Jupiter. When the joint Soviet-American mission on the Leonov was planned instead, Curnow was one of the three American experts to go on the trip along with Heywood Floyd and Dr. Chandra.
Curnow was one of the first people to set foot on Discovery again, along with Maxim Brailovsky. His engineering expertise managed to get Discovery working again.
Curnow is described in the book as a large bear-like man, who was naturally loud and tended to be the life of the party. He was bisexual and briefly had a relationship with Maxim Brailovsky, until Floyd told him to break it off for the sake of crewwoman Zenia Marchenko, who was in love with Max. Following his and Max's break-up he became an item with Dr. Katerina Rudenko, who he married once they came back to Earth. In the movie Curnow is played by John Lithgow, and he is a very blunt man who is not as popular with the Russians as his novel counterpart. Also, in the film he is never romantically attached (as it was still controversial in 1984, his bisexuality was never factored into the movie) and his relationship with Max is slightly adversarial.
Despite being younger than Heywood Floyd, Curnow apparently died some time before 2061 - as did everyone on the Leonov except for Floyd and Zenia Marchenko.