Primordial Black Holes are black holes that could have been formed in the very early Universe and are arguably the most economical candidates for Dark Matter. But to make precise estimations of their abundance, it is essential to accurately know the initial conditions that could lead to their production. In this seminar, I will describe the current standard formalism and methods to accurately predict the necessary initial conditions for black hole formation, including the consequent numerical results from simulations of the collapse of adiabatic fluctuations generated during inflation. Moreover, I will present new results on the simulation of the formation of false vacuum bubbles, which can be produced if the inflaton becomes trapped during inflation. These localized bubbles will eventually end up forming black holes, also called baby Universes.