This chapter introduces the background of HONN model developing history and overview 24 applied artificial higher order neural network models. This chapter provides 24 HONN models and uses a single uniform HONN architecture for ALL 24 HONN models. This chapter also uses a uniform learning algorithm for all 24 HONN models and uses a uniform weight update formulae for all 24 HONN models. In this chapter, Polynomial HONN, Trigonometric HONN, Sigmoid HONN, SINC HONN, and Ultra High Frequency HONN structure and models are overviewed too.