The POSIX-standard comm utility can do this also.

• -2 suppresses lines from the second argument (file1)
• -3 suppresses lines appearing in both files

Assumes that file1 and file2 are already sorted. If they are not, you can use process substitution to do so:

comm -23 <(sort file2) <(sort file1)

Process substitution is a bash-specific feature (also available in zsh but with a different syntax).