They're not made up of anything smaller. But for protons and neutrons, it doesn't stop here. Only the up and down varieties are important in protons and neutrons. The other quarks can make up particles similar to protons and neutrons, but usually heavier. These particles decay almost immediately after they're created, and so we're not going to talk about them here.
Gluons are particles which bind quarks together to form protons, neutrons, and other stuff.
So we're left with the following picture, which should not be taken too seriously. It's only here to show you the levels of structure in an atom. It looks like an atom about as much as a weather map full of jagged lines, giant L's and H's, and a puffy cloud with a golden thunderbolt looks like the sky. Anyway, quarks and gluons aren't made up of anything smaller that we can tell. Which means, that's it.