Hypothesis of primordial black hole creation in the early Universe was formulated by Ya.B. Zeldovich and I.D. Novikov in 1966 year. In the recent years this hypothesis becomes extremely heightened and popular. Modern astronomical data in the electromagnetic spectrum and also observation of gravitational waves and cosmic neutrino reveal the series unique astrophysical phenomena, which may be directly related with primordial black holes, created before the formation of first stars. This review is devoted to description of different models of primordial black holes formation and also to elucidation the astronomical and astrophysical methods for a verification of primordial black hole models. In particular, we describe in details the formation of primordial black holes and their clusters during gravitational collapse of the so called domain walls in the early Universe with additional space-time dimensions.