Primordial black holes, hypothetical objects that may have formed in the early Universe through the interplay between high-energy physics and gravity, are very appealing candidates for dark matter. In this seminar, I will investigate their formation as the result of the collapse of energy density fluctuations originating from supercooled first-order phase transitions. I will show the results of a simplified approach, where the energy density fluctuations are evolved within the limit of the flat FRW Universe. We will discuss how these results are modified when the full covariant formalism of cosmological perturbation is adopted. Finally, I will present ongoing development in this field and its prospects.