This article discusses the optimization of training signals for highly accurate mathematical descriptions of simultaneous non-linear and dynamic effects for behavior modeling and digital predistortion techniques for RF power amplifiers. Coefficient reduction techniques are described for polynomial model and neural network structures. Training signal design makes use of white noise, multitones, modulated signals, stratified signal and systematic sampled datasets, and symbol constellation mapping techniques to characterize the PA, and these various approaches are rigorously described and compared. Finally, approaches to the training signal optimization are described and experimental results are presented.