Hitting <return>, <enter> or <spacebar> is like clicking the Go button unless there is a suggestion arrow showing, then it will make the move.
Hitting <esc> will clear any move suggestions, dismiss any feedback on the board as well as cancel engine thinking without getting a move back.
Adding <shift> or <option> to Previous or Next Puzzle will move 10 or 100, respectively in that direction.
Other Hot-Keys<option> + '1' will take you to the first collection
<option> + '[' will take you to the previous collection
<option> + ']' will take you to the next collection
<option> + 'B' will cycle through the different board styles
<option> + 'P' will start a new game