Since Smarter Search for Bitbucket is powered by Elasticsearch. It utilizes Elasticsearch's powerful Query String Syntax. This includes support for wildcards, regular expressions, fuzziness, and much more.
There are also many advanced filtering options. Here is a brief summary:
Search code, filenames and commits
Filter results to only code, commits, or filenames
Filter results to specific projects
Filter results to certain slugs.
Filter results to certain refs
Filter results to certain file extentions
Author/editor names or emails
Filter results to a specific author
Committed on or after/before (Commits only)
Filter results to a certain date range.