Share history between panes/windows

Add these options to your .zshrc:

setopt inc_append_history

I also find hist_ignore_dups hist_ignore_space useful.

See also Zsh » Options » History.

shell history has precious little to do with tmux, it has to do with the shell you are using. So if you chose to use zsh it is enabled iirc by default. With bash you need to add some magic to your .bashrc

export PROMPT_COMMAND="history -a; history -n"

this appends your last command to history and reloads your history after each command. See this post for more information.