How do I make Vim do normal (Bash-like) tab completion for file names?

Question

When I\'m opening a new file in Vim and I use tab completion, it completes the whole file name instead of doing the partial match like Bash does. Is there an option to make

Answer 1

The closest behavior to Bash's completion should be

set wildmode=longest:full,full

With a few character typed, pressing tab once will give all the matches available in wildmenu. This is different to the answer by Michael which opens a quickfix-like window beneath the command-line.

Then you can keep typing the rest of the characters or press tab again to auto-complete with first match and circle around it.