The scattering of electromagnetic waves by precipitation particles and their propagation through precipitation media are of fundamental importance in understanding the signal returns from dual-polarized, Doppler weather radars. In this chapter, a number of useful concepts are introduced from first principles for the benefit of those readers who have not had prior exposure to such material. Starting with Maxwell's equations, an integral representation for scattering by a dielectric particle is derived, which leads into Rayleigh scattering by spheres. The Maxwell-Garnet(MG) mixing formula is discussed from an electrostatic perspective (a review of electrostatics is provided in Appendix 1). Faraday's law is used in a simple example to explicitly show the origin of the bistatic Doppler frequency shift. The important concepts of coherent and incoherent addition of waves are illustrated for two- and N-particle cases. The time-correlated bistatic scattering cross section of a single moving sphere is defined, which naturally leads to Doppler spectrum. The transmitting and receiving aspects of a simple Doppler radar system are then explained. This chapter ends with coherent wave propagation through a slab of spherical particles, the concept of an effective propagation constant of precipitation media, and the definition of specific attenuation.