Black-box or behavioral models (BM) are obtained from input/output observations of a system, without knowledge of its inner structure. They can be optimized for a specific system, and so it is possible to represent the physical component behavior by this model (e.g., RF power amplifiers). The principal applications of PA BMs are linearization and circuit simulation tools. PAs are nonlinear devices with memory effects, therefore, it is a challenging task to extract their equivalent BM. The work starts with a brief overview of BMs excitation signals and partitioning of data used in the modeling process. Figures of merit, tools to measure BMs quality, are analyzed. An investigation of linear estimation techniques and parametrization of linear systems is also performed, showing advances in the finite impulse response filter estimation. Following, techniques for nonlinear systems estimation are described, focused on PAs. Static nonlinear models and dynamic ones are outlined, together with their linear estimation methods. In the second part of this work, selected applications of behavioral models are surveyed.