A review is given of the physical phenomena observed when polyatomic molecules interact with intense infrared radiation pulses. A brief historical account is given of earlier investigations and the main processes are classified. Then, the following topics are considered: 1) multiphoton infrared absorption and transition of molecules through lower vibrational levels; 2) dynamics of molecular excitation in a vibrational quasicontinuum and distribution of the vibrational energy between the modes and levels; 3) dissociation of highly excited molecules. The main experimental and theoretical results, and possible future trends are discussed. The review concludes with a brief list and illustrations of typical applications of the phenomena described in molecular spectroscopy, chemical physics, nuclear chemistry, and chemical synthesis.