I've seen various tap storage things around but they tend to only have space for a taper tap, a second (aka plug) tap and a bottoming (aka plug) tap. That leaves nowhere for spiral flute, spiral point, serial taps, fluteless taps and long series taps. To deal with that, I made my own. It only holds metric coarse taps, but the metric fine ones come out rarely enough that I don't mind rummaging in one big drawer. Antediluvian nonsense like BSF or UNC come out even more rarely so the same applies.
Unit was knocked together out of plywood and is a bit shabby really, but it does the job.
This shows one of the drawers. The debossed text showing what's in each pocket is a bit scruffy, but it's readable. The handle and the (embossed & two-colour) drawer label are dovetailed in. The drawer labels weren't a fantastic fit but they do the job - I think it might be because I printed them with a different (0.25 mm) nozzle size.
These are the smaller ones. I don't have as many types of tap for the really small ones (and mainly only use serial taps for M2 and M2.5). There is also a drawer for thread gauges and some spare taps.
The smaller tap wrenches and die stocks I have live in the bottom drawers; the bigger ones wouldn't fit in this unit so they go in a different drawer unit.