Solitons and solitary waves in inhomogeneous media are of interest in relativistic quantum mechanics and quantum electronics, e. g. in research on infrared soliton lasers. After a short introduction to soliton mathematics the authors present a theoretical study on solitons and solitary waves in inhomogeneous one-dimensional nonlinear media on the basis of nonlinear Klein-Gordon equations modified by spatial variations of refractive index and anharmonic potential. Special emphasis is on periodic modulations. Various approaches and approximations have been applied to find solitary-wave and soliton solutions. Typical solutions are illustrated in order to demonstrate their characteristic features.