This text starts with the basic principles of electromagnetic scattering, thermal emission and transmission in discrete scatters and continous random media. It discusses some of the most comprehensive approaches of the vector radiative transfer theory, wave analytic theory in random media, numerical models and applications in both active and passive remote sensing of the atmosphere and earth terrain surface, such as vegetation canopy, snow and ocean. The text contains the author's research work on quantitative modelling for remote sensing, as well as some advances made by other colleagues. It aims to provide readers with an overall set of the basic theories and equations, models, numerical approaches and applications. Graduate students and researchers should find this work useful either as a textbook or reference book.