Your Borrowing History is a static, raw list in your account that cannot be manipulated. However, if you have transferred your Borrowing History to your Completed Shelf, you can sort that list using the "Sort by” drop down menu, and you can filter using the options on the left side of the screen. You can also add private notes about titles, or add tags that will help you filter your list. Searching is not currently possible, but sorting, tagging and filtering are helpful.
Exporting is not currently available from your raw Borrowing History list or Completed Shelf, but your reading history can still be exported from your account in Classic Catalog.