Primordial black holes (PBHs) have attracted significant attention from many aspects in recent years. In this seminar, I will review the basics and recent progress in the dynamics of PBH formation. I will begin with a brief review of the standard setup for PBH formation scenarios, followed by an analytical PBH formation model based on applying the Jeans criterion to a 3-zone model. I will then discuss spherically symmetric simulations of PBH formation in a radiation-dominated universe, covering numerical techniques, comparisons with threshold models using the compaction function, critical collapse, and the characteristics of Type I/II and Type A/B PBH formations. Furthermore, I will highlight recent developments in non-spherically symmetric PBH formation simulations. Finally, I will address our recent study on PBH formation during a matter-dominated era.