I made that list for myself, maybe it can help other figure what to 
think when we write about search engines:

     - crawler e.g: apache nutch, possibly with headless browsers support 
and feeds (atom, rss, sitemap, robots.txt)
     - boolean keyword, full-text search to conceptual search
     - entity linking (aka. wikification) and disambiguations
     - one-way or two way synonyms and other lexicographic features
     - last few days weeks or month search (like google tools)
     - trends and trending topics (zscore)
     - alerting
     - domain search ie. restrict search to a given domain / subdomain
     - spell checking, transliteration and soundex
     - multi-lingual
     - autocomplete, query suggestion
     - more-like-this
     - network topology e.g. incomings links, outgoing links, page rank
     - caching, offline use, archiving
     - image and video search
     - code search
     - question answering e.g. how big is the Everest?
     - "response extraction" extract answer to query from top results
     - summary
     - oembed
     - readability metrics, privacy metrics (no third party cookies or 
analytics, no javascript, small size...)
     - maps
     - book OCR
     - safe search
     - voice search (mozilla common voice)
     - deep search / full index scan


Chime in!