Electromagnetically induced transparency (EIT), a typical quantum interference effect, has been extensively investigated in coherent atomic gases. In recent years, it has been recognized that the plasmonic analog of atomic EIT, called plasmon-induced transparency (PIT), is a fruitful platform for the study of EIT-like propagation and interaction of plasmonic polaritons. Many proposals have been presented for realizing PIT in various metamaterials, which possess many unique characters, including the suppression of absorption of electromagnetic radiation, the reduction of propagation velocity, etc. Especially, nonlinear PIT metamaterials, obtained usually by embedding nonlinear elements into meta-atoms, can be used to acquire an enhanced Kerr effect resulted from the resonant coupling between radiation and the meta-atoms and to actively manipulate structural and dynamical properties of plasmonic metamaterials. In this article, we review recent research progress in nonlinear PIT metamaterials, and elucidate their interesting properties and promising applications. In particular, we give a detailed description on the propagation and interaction of nonlinear plasmonic polaritons in metamaterials via PIT, which are promising for chip-scale applications in information processing and transmission.