According to Penrose's singularity theorem, gravitational collapse under the strong energy condition inevitably leads to the formation of a spacetime singularity once an event horizon forms. The presence of a singularity indicates that general relativity is no longer applicable for describing such extreme conditions. This has led to growing interest in so-called regular (nonsingular) black holes. To avoid the singularity predicted by Penrose’s theorem, matter preventing its formation must violate the strong energy condition. However, in massive stars prior to collapse, we do not observe any matter that violates this condition. As a result, such exotic matter must emerge dynamically during the gravitational collapse itself. In this talk, key issues related to the formation of regular black holes will be discussed. The process of gravitational collapse of a star composed of baryonic matter will be considered, and possible mechanisms explaining the emergence of a regular core and matter violating the strong energy condition will be proposed. It will be shown that under certain physical conditions, gravitational collapse can lead to the formation of Dymnikova-type or Hayward-type regular black holes. Additionally, potential observational signatures of these objects will be addressed.