Given a Calabi-Yau 3-fold, coming, e.g. from Batyrev's construction, what can we compute about it? In this talk, we explore some things we can compute, some things we can in principle compute, and things we would like find algorithms for. We start with the Picard group, Hodge numbers, and some intersection theory. We describe CTC Wall's result which basically allows us to tell when two of these are the same topologically (homeomorphic or diffemorphic), and we show that we can compute (for small h^(1,1)(X)) these. We then turn to cohomology of divisors and sheaves, as well as birational geometry: can we compute flops, nef cones, Mori cones, effective cones? These are often infinite objects, so is this even possible!? (these notions will be defined or at least made explicit!) The parts of this talk that are new have been done with Liam McAllister (Cornell, String theory), and several other physics collaborators.