Constraints on the formation of primordial black holes - especially the ones which are small enough to evaporate - provide unique information about the early universe and high energy physics. They could also be a useful probe of dark matter, dark energy and dark dimensions. In this talk I will review some of the constraints discussed in my recent paper with Kohri, Sendouda and Yokoyama. For evaporating black holes, the dominant ones are associated with big bang nucleosynthesis and the extragalactic photon background, but there are also other limits associated with the cosmic microwave background, cosmic rays and various types of relic particles. For larger non-evaporating black holes, important constraints come from their gravitational and astrophysical effects.