When coupling molecules with quantized radiation modes inside an optical cavity, a set of new photonmatter hybrid states are created due to the coupling between the molecules and the quantized radiation field. These new created hybrid states, which are commonly referred to as polaritons, have been shown to facilitate new chemical reactivities and selectivities. Theoretical investigations play a crucial role in understanding the fundamental limit and basic principles in this emerging field, as these polariton chemical reactions often involve a rich dynamical interplay among the electronic, nuclear, and photonic degrees of freedom (DOFs).