Selecting Edit > Strip Silence from the region context menu will detect silence (based on a user-chosen threshold in dBFS), split a region based on the boundaries of the silent segments, and remove the silence. You can also specify a minimum length for silence, which can useful when editing very percussive material and just needing to automatically trim the ends of a region. The dialog looks like this:
The edit will be carried out on all selected regions, allowing batch processing. You can also see in the screenshot how the main editor window is used to show silent segments and report the number and durations of the shortest segments.