In the application of nuclear radiation, the problem of the transport of photons and neutral or charged particles through the matter is central for understanding the physics of the process, for a correct interpretation of the measurement and for a convenient choice of instrumental operating conditions. This paper, in the first part, is intended as a survey of the genesis of the transport equations, which describe the phenomenon of the diffusion of the particles. With a regressive procedure, it is possible to obtain the commonly used transport equations directly from Liouville equation; the approximations that must always been involved can be related to two dimensionless parameters if suitable dimesionless variables are introduced. In the second part, approximate solutions of Boltzmann and Fokker-Planck equations are given for particular physical situations of interest in x-ray spectroscopy and electron microprobe analysis.