The threaten of extreme waves is clearly explained by reviewing some marine accidents related to naval architecture and ocean engineering, which give rise to a substantial need to develop a few reliable and computationally efficient numerical tools for the study of extreme waves. The mechanisms of generation of extreme waves are various and complicated. Besides the linear superposition of Fourier components with coherent phases and strong wave-current interaction or wave diffraction, it has been established that the modulational instability of waves can explain many features of the dynamics of extreme waves. Various numerical wave models that can represent the nonlinear focusing have been briefly discussed, starting from the simplest cubic nonlinear Schrödinger equation to the fully nonlinear CS model. Besides, a series of statistical and probability models, frequently used to analyse the properties of extreme waves in irregular sea states, are also reviewed in an ascending order based on the nonlinearity.