The Speed-gradient approach to building dynamical models of physical systems is described. It is based on the Speed-gradient principle: Among all possible motions only those are realized for which the input variables change proportionally to the speed gradient of appropriate goal functional. Application of the principle is demonstrated by examples: motion of a particle in the potential field; wave, diffusion and heat transfer equations; viscous flow equation. Based on the Speedgradient principle the proof of the Onzagger principle from thermodynamics and its extension to a class of systems far from equilibrium are given.