This survey is devoted to the significant role of various dry friction laws in engineering sciences. Both advantages and disadvantages of a frictional process are illustrated and discussed, but excluding the nature of friction. It is shown how the classical friction laws and modern friction theories exist in today’s pure and applied sciences. Static and dynamic friction models are described. An important role of purely theoretical and experimental investigations in developing the appropriate friction models is outlined, placing an emphasis on new approaches (models proposed by Bay-Wanheim, Dahl, Bliman-Sorine, Lund-Grenoble, as well as atomic scale and fractal models, among others). Friction treated as a complex process being in interaction with wear, heat emission, and deformation is also discussed. Then the impact of dry friction models on current dynamical systems theory is reviewed. Finally, an application of friction to model a brake mechanism as a mechanical system with two degrees-of-freedom, including experimental and numerical analyses, is given. This review paper contains 254 references.