Even without external photon pumping, cavity vacuum fields can be strongly coupled with molecular transitions (electronic excitation and molecular vibration), resulting in the formation of polaritonic states. The energy states of molecular systems are altered under strong coupling, revealing intriguing phenomena, such as improvements in energy/exciton transfer and modulation of chemical reactions. In this review, we highlight recent advances in cavity strong coupling, including exciton strong coupling and vibrational strong coupling, from a chemistry-based viewpoint.