In this talk we shall present an historical survey of the conceptual and computational developments which led to the formulation of the Lattice Boltzmann (LB) method; from its statmech foundations (Lattice Gas Cellular Automata) to present-day leading edge scientific and engineering applications across a broad range of scales and regimes of motion. From large scale turbulent flows, to micro-nanofluids all the way down to quark-gluon plasmas and, recently, quantum computing for fluids as well. These developments, spanning over three decades in time, witness to the outstanding power of (lattice) kinetic theory as a privileged mathematical and computational framework for the quantitative study of complex states of flowing matter far from equilibrium and its multiple applications to modern science and engineering, A remarkable success story that falls perfectly within Eugenio Beltrami’s great legacy.