Theoretical study made by the author’s group on wave propagation in crystalline solids at finite temperatures from a microscopic and statistical-mechanical point of view is reviewed. After explaining the derivation of the basic equations for the wave propagation in anharmonic lattices, some typical waves are analyzed on the basis of the equations and their characteristic features are discussed. Waves studied are weak and short waves, acceleration waves with singular surfaces, ultrasonic waves, waves excited by impulsive forces, and shock waves. Interesting studies remained to be taken up are also summarized.