If you’d like some vim-like bindings in tmux, you can turn on vi mode. To do so, add the following line to your .tmux.conf file:

setw -g mode-keys vi

With this added and tmux re-sourced, you’ll now have a variety of vi-like bindings. For instance, when in tmux’s copy mode, you can now use v to begin making a visual selection and y to yank that selection into tmux’s copy buffer.