We present a lightning overview of the implications of primordial black holes on cosmological and astrophysical evolution, from the early to the late observable Universe, with emphasis on the cosmic dawn and reionization epochs and on hierarchical large-scale structure formation. We discuss how primordial black holes may affect dark-matter halo evolution, star formation, supermassive-black-hole formation, and how they may interact with particle dark matter. Meanwhile, the primordial black holes themselves evolve via accretion, emission and mergers.