The way it's likely seen by many tech companies is that the more decisions you have to offload to the user, the less advanced your system is. An old car with a lot of knobs and dials and levers is not more advanced than a self-driving car with a single control, select destination. Some people will still prefer the old car, but it will be a niche market.
"You're viewing through FOOBAR lens. Click here to view results from another lens".
Doesn't have to be that complicated.
You can add three more buttons on top of the tabs that are already there, but would their value for more advanced users be worth the extra friction/confusion for average users? And how would it scale if someone wants a fourth, fifth, or tenth "lens"?
Try images.yandex.com: it's vastly better than most others. It's not too good at identifying specific people but it will find prior exact uses of an image (like TinEye) but is especially very good at abstracting what's the abstract subject, color, pose, setting etc in a photo and show you similar.
The question is if such an approach would lure a lot of people away, I could see an entry angle might be a front end to google with an app that does that.
We now have a couple digital generations of folks who've grown up with 'web', and we've generated billions of 'documents'.
TIME ACCURATE QUERIES need to be mainstream.
"Let me search for FOOBAR and get results that would have been accurate/returned for Dec 11, 2006. Now search for FOOBAR and get results from Dec 11, 2014", etc.
Create 3-5 different search algorithms, with names and understandable characteristics, then let me choose which one when searching. You may have some algorithm that prioritizes recency, or rapid changes, or more interaction, and others that prioritize longevity, citations/links, others that prioritize that type of information - prioritize regional or noteworthy events over historical info, etc. Have some algorithms that penalize spam/linkfarms more heavily than others. The git/so spam farms that come up when I search for an error message are simply useless, and would love ways to switch away and try other algorithms, without necessarily having to switch entire search systems.
Have algorithms that explicitly take in to account the search/click behaviour of others. Let me choose to have the search behaviour of friends/colleagues/famous-folks explicitly included or excluded in search results ranking.
Let people easily switch between multiple algorithms, and let 1000 gardens bloom (or something like that).
Also, determining better ways to 'search' non-text stuff. If virtual worlds become a thing, finding ways to 'search' those (whatever that might mean) will be big.
Image search still has a long way to go, IME.