Ultracold atoms have achieved many outstanding successes in a wide variety of experiments, many of which utilize the exquisite control over collisions that is possible with tunable scattering resonances. The availability of cold molecules should greatly extend the range of experimental possibilities. This talk will emphasize some simple and essential concepts for understanding the similarities and differences between ultracold atomic and molecular collisions in gases and lattices. Both atomic and molecular collisions can be described in terms of a similar framework, based on the separation of energy, time, and distance scales associated with short range and long range interactions. The properties of the interacting species and the long range potentials determine the spectrum of bound and scattering states, and the available resonances, over a relatively wide range of energy near a collision threshold. This is readily illustrated for neutral atoms. Atoms and molecules differ in the nature of their long range potentials and the spectrum of the \"collision complex\" they form. It is often convenient to summarize ultracold elastic and inelastic collisional properties by a complex scattering length, which accounts for both the coherent interactions and the collisional loss processes. Although molecules typically have more and stronger loss channels than atoms, molecules should prove to be especially useful in lattice experiments, where they can be protected from \"bad\" collisions.