This article synthesizes a number of studies involving both quantitative characterization of precipitate microstructures (size and volume fraction) and modelling of precipitation kinetics. The main experimental methods used are Small Angle X-ray and Neutron Scattering and Transmission Electron Microscopy. The modelling is based on semi-analytical models (coupled differential equations) and on numerical models (based on the discretization of the precipitate size distribution). A variety of systems are studied, both aluminium alloys and steels. After considering isothermal precipitation, the issues of dynamic and non-isothermal precipitation are discussed. Finally, precipitation phenomena occurring during welding are characterized.