The advent of ultracold molecules opens the possibility to explore chemical reactions with perfect control of the quantum states of the reactants. We report on several surprising results of our work with ultracold NaLi molecules. First, we demonstrate a factor of 100 control of reaction rates between NaLi molecules and Na atoms by changing the atom's spin state. This ability to slow reactions allowed us to demonstrate sympathetic cooling of molecules for the first time. Next, we explore two very different collisional resonances. A resonance in NaLi+Na reactions exemplifies the standard description of chemical resonances. The other, for NaLi+NaLi, is the first ultracold molecule-molecule resonance observed and runs completely counter to the standard description. Simple models relate the complex chemical dynamics to the simple physics of a Fabry-Perot resonantor and point a number of open questions in chemical dynamics that can be explored with ultracold molecules.