This paper describes EEG signal simulation methods. Three main methods have been included in this study: Markov Process Amplitude (MPA), Artificial Neural Network (ANN), and Autoregressive (AR) models. Each method is described procedurally, along with mathematical expressions. By the end of the description of each method, the limitations and benefits are described in comparison with other methods. MPA comprises of three variations; first-order MPA, nonlinear MPA, and adaptive MPA. ANN consists of two variations; feed forward back-propagation NN and multilayer feed forward with error back-propagation NN with embedded driving signal. AR model based filtering has been considered with its variation, genetic algorithm based on autoregressive moving average (ARMA) filtering. © Springer International Publishing AG 2016.