https://en.wikipedia.org/wiki/The_UNIX-HATERS_Handbook

That's standard POSIX.

Tilde expands when at the beginning of an unquoted word.

Pretty straightforward.

  ~ or ~/ --> $HOME

  ~user --> user's home

Bash has a few extra.

  ~+ --> $PWD

  ~- --> $OLDPWD

  ~+N or ~-N --> dirs

well.. it's in zsh (and probably any other *sh) too