Built in search features of MediaWiki may not be sufficient for some use cases, you might especially be intereted in
- the possibility of searching for semantic properties or doing facetted search (search that can be narrowed down by semantic properties)
- the possibility of searching inside the contents of uploaded files (e. g. PDF documents)
- the possibility of including search results outside of your (Semantic)MediaWiki instance (e. g. other Websites/Wikis or documents resinding on a filesystem)
- Browsing interfaces provides an overview of built in options of SMW, most of them are not quite suitable for the occasional user of an SMW powered site, but more targeted to power users.
- Semantic Result Formats provides the "filtered" format
- Semantic Drilldown provides a different possibility of a faceted search
- Semantic Forms can be used to define query forms. You can customize the fields you want to provide for searching to the users as well as the results to be displayed
None of these options provide the possibility to include sources from outside of the wiki.
- A comparison of search options is available here: https://www.mediawiki.org/wiki/Extension:SphinxSearch#Comparison_matrix (some entries are outdated)
- MWSearch and Lucene search use by Wikimedia to 2014, suitable for large sites
- SphinxSearch a search extension, a better option for smaller sites, powered by Sphinx Search
- CirrusSearch will replace MWSearch for Wikimedia sites, implements search powered by https://en.wikipedia.org/wiki/Elasticsearch