This article focuses on the history of theoretical ideas but also on the developments of experimental tools. The experiments in our laboratory are used to illustrate the various developments associated with Brownian movement. In the first part of this review, we give an overview of the theory. We insist on the pre-Einstein approach to the problem by Lord Rayleigh, Bachelier, and Smoluchowski. In the second part, we detail the achievements of Perrin, measuring Avogadro's number, quantifying the experimental observations of Brownian movement, and introducing the problem of continuous curves without tangent, a precursor to fractal theory. The third part deals with modern application of Brownian movement, escape from a fixed optical trap, particle dynamics on a moving trap, and finally development of Brownian thermal ratchets. Finally, we give a short overview of bacteria motion, presented like an active Brownian movement with very high effective temperature.