Box filters are air driven and great for mechanical filtration (in addition to some bio, depending on what you put in them):
https://www.jehmco.com/html/box_filters.html
Coupling box filters with sponge filters is a great way to reduce the frequency of having to clean the sponges (which is a PITA). I run a bunch of air through the box filters (which have some gravel in the bottom and pillow stuffing from Michaels) and less air through the sponges (because bio works better with less flow and so that they don't get clogged as frequently). I also use a lot of Poret (with relatively low flow). I clean the box filters (dump out the gunk, replace dirty fluff with clean) as I'm refilling tanks during weekly water changes.
Nearly my whole fishroom is run on a couple of air pumps. I don't use HOBs, canisters, etc. to reduce power consumption and because they're pains to clean.