Primordial black holes are black holes that may have formed in the early Universe. Their masses span potentially a range from as low as the Planck mass up to many orders of magnitude above the solar mass. Besides their conceptual importance regarding our understanding of quantum effects and gravity, they may provide the dark matter. In order to constrain this possibility, a proper understanding of their formation mechanism is crucial. In my talk, after a general introduction on primordial black holes, I will discuss recent investigations on this issue, including so-called critical collapse, non-sphericity and non-Gaussianity. Furthermore, I will discuss how to properly compare extended primordial black-hole mass spectra to observational constraints, such as those deriving from recent microlensing surveys.
