When on the search page you will see a Search History tab up at the top:

REsearch will remember the last 50 unique searches and include a time stamp of the most recent run.

Clicking the Search History tab will open up a Recent Searches window:

You may also save searches from this window:

The saved search will be displayed within the Recent Searches window (as long as it doesn’t get bumped off) and also accessible from your My Saved Searches.