This book presents new research results on channel characterization and modeling. MIMO channel characterization and modeling techniques are investigated. The first part exposes a generalized and systematic representation of systems and channels in the spatio-temporal domains. It is a generalization of the concepts introduced in the research literature: it consists of a set of sixteen kernel functions and eight system functions, in time, frequency, space and wave-vector domains. A series of examples illustrates the concept. In the second part, a space-time signal measurement technique is introduced along with a wave-vector-frequency spectrum estimation method. These are employed to create a large virtual antenna array from a small number of antenna elements. A new calibration technique to estimate measured wave vector spectra is presented. In the last part, a generalized view of the Doppler phenomenon, based on the characterization technique is presented. Here, the Doppler spectra, caused by scatterer mobility under different scatterer velocity distributions, are investigated. Fixed-wireless scenarios, with stationary transmitters and receivers with mobile scatterers are analyzed.