Abstract: In this talk, I will give an overview of primordial black holes, from their origins to their present role in early-Universe cosmology. I will focus in particular on my research on PBH formation, highlighting some of the main results and developments achieved so far. I will then discuss open problems and future research directions, including connections with gravitational-wave cosmology. Finally, I will discuss how these research directions could fit within and contribute to the research activities in cosmology and gravitation at the ICC/UB.