I think people use storage techniques that are handy and appropriate for their situations.
For a lot of small stuff, I'll use small manila envelopes (about 1.5" x 3"). For my collection of 0805 resistors, I have one small envelope for each value. The group of small envelopes goes into a larger envelope labeled "0805 resistors". Same for the 1206 resistors, my SMD caps, etc.
For semiconductors, especially smaller SMD ones, I keep them in the ESD bag that they come in, and attach that to the cover page of the datasheet. Then I keep these in 3-ring binders organized by type of semiconductor (i.e. diode, zener, TVS, npn BJT, pnp BJT, N mosfet, P mosfet, op-amps, comparators, voltage regulators, etc.).
Big, bulky items end up in an old tackle box or other container. These aren't as well organized. :-(
If I've got parts kitted up for a project, these will end up in a zip-loc bag or storage tub of some kind, along with calculations, notes, datasheets, circuit boards, etc.
The important thing is to have a system that avoids blowing parts all over the lab when you sneeze.
Steve K.