can't find zsh history on OSX 10.8.5

When I log into the Terminal app on OSX my default shell is /bin/bash. Entering echo $HISTFILE points me to /Users/monkeybrain/.bash_history and head $(echo $HISTFILE) shows me that the file contains history entries.

If I then type zsh to switch shell a couple of weird things happen. Firstly even though my prompt changes (so it looks like I'm in the new shell) my $SHELL environment variable still points to /bin/bash. The $HISTFILE variable is now empty, and there is no such file as ~/.zsh_history. Also, I can't use Ctrl-A or Ctrl-E to move through the command line.

What's happening here?

Many thanks,

MB