Joseph Boussinesq (1842-1929): a pioneer of mechanical modelling at the end of the 19th Century. Soils, granular media, civil engineering. Bifurcations in granular media: macro- and micro-mechanics approaches. Use of the Boussinesq solution in geotechnical and road engineering: influence in plasticity. Boussinesq equation, elasticity, beams, plates. On Boussinesq's paradigm in nonlinear wave propagation. From Boussinesq-Love contact to impact between hyperelastic bodies. Two dimensional Boussinesq equation in a disc and anisotropic Sobolev spaces. Boussinesq equation, surface waves in fluids. Dissipative Boussinesq equations. J. Boussinesq and the standing water waves problem. Unsteady flows, turbulent flows. Interactive boundary layers in turbulent flow. On the history term of Boussinesq-Basset when the viscous fluid slips on the particle. About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. Boussinesq approximation, convection. Boussinesq approximations, and beyond, in a tall thermo-gravitational column. The Rayleigh-Benard problem in extremely confined geometries with and without the Soret effect. Boussinesq approximation, geophysical flows. Generalizing the Boussinesq approximation to stratified compressible flow. Internal gravity waves: parametric instability and deep ocean mixing.