I store by theme. I have around 3-4 copies of each set since Ruins of the Wild, so it would be pretty cumbersome otherwise.
The tiles are in
IKEA boxes by general theme (Dungeon, Dire Tombs, City, Wilderness, Caves).
Within these boxes, I have the tiles in Ziploc bags based on type.
So, within the Dungeon box, I have a bag of doors, a bag of stairs/ladders, a bag of furniture, a bag of weird elemental tiles, etc.
Tiles bigger than 4x4 are just free in the boxes - they're not too tough to sort through.
So far it has made it very easy to manage the tiles, both for prepping things in advance and improvising encounters at the table if things go differently than planned. We game in a fixed place in my house, so transport isn't an issue, but the tiles are stored well enough that it wouldn't be to tough to put the boxes in a back seat.