Can you put black powder in modern shells to shoot through old shotguns?

You can, but you should be careful about the chamber length. For example, the most common length for modern 12 gauge shells is 2 3/4", but older shotguns may only be chambered for 2 1/2" shells. So long as the chamber length is ok, it is certainly possible to load and shoot black powder with modern hulls. Appropriately sized plastic wads can also be used (I've used Winchester red AA wads with AA hulls, 80 grains of powder, 1 oz. of shot). You do tend to get some stringy plastic residue that has to be cleaned out of the bore. I've actually switched to using brass shotshells for black powder now.