This chapter contains the discussion on fundamental concepts related to nonlinear model identification. First, linear in parameter model identification techniques are presented. This covers static and dynamic systems. Following that, the idea of developing nonlinear models in the framework of Orhonormal Basis Functions (OBF) is described. In Sect. 3.3, basic theory of neural networks and fuzzy systems are elaborated. In the state of the art designs, one of them is constructed in the structure of the other allowing the development of a transparent model that can be trained with relatively minimal effort. Section 3.4 is dedicated to the discussion of nonlinear system identification using combined version of neural networks and fuzzy systems. Last section of the chapter deals with three different model training algorithms Least squares based, back-propagation and particle swarm optimization. © 2018, Springer International Publishing AG.