Loose parts and small bits sprue with multiple parts on it go into one of my many spares boxes, most of which are simply boxes of kits I’ve built. Some parts that make up a complete subassembly, like an engine, I cut off the sprue and put into a plastic bag, which then goes into the box (with the contents written on with a marking pen). If I have (nearly/mostly) full sprues left, I put those in a box without taking the parts off, because then it’d be a nightmare trying to find them all again.
This is organised per subject, for those I’ve built a lot of over the years: I have a box with M113 parts, one with M26/M46/M47/M48/M60 parts, two with Sherman parts. Most of the rest goes into a big box of miscellaneous parts, or into one of the two I have with just wheels and tracks.
I also have some of those small sets of drawers and a couple of plastic boxes with many compartments inside, which I use for similar parts: a compartment full of headlights, one with periscopes, one with radios, a drawer with American WWII weapons, one with tools, etc.
All this proved necessary because it first of all became impossible to stuff all the parts into a single box, and then to find things in the box(es) with everything mixed up. That can still be a problem, of course, especially if I’m after parts for a vehicle I’ve only built maybe one model of, but nowhere near as bad as when I still had everything mixed up.