Is there a fundamental layer of objects in nature? And if so what sorts of things populate it? Among those who answer ‘yes’ to the first question, a common answer to the second is ‘atoms,’ where an atom is understood in the original sense of an object that is spatially unextended, indivisible, and wholly lacking in proper parts (whether actual or potential). Here I explore some of the ontological consequences of atomism. First, if atoms are real, then whatever motion they appear to undergo must be discrete (discontinuous). The link between atomism and discrete motion goes back at least to Aristotle and is admitted by some atomists, but the full significance of that admission has been neglected. I argue that a commitment to discrete motion in turn entails significant and sometimes counter-intuitive results. I also examine the implications of these results for the philosophy of mind and for discussions of metaphysical naturalism.