This book provides an overview on the current state-of-the-art research on non-linear option pricing. Non-linear models are becoming more and more important since they take into account many effects that are not included in the linear model. However, in practice (i.e. in banks) linear models are still used, giving rise to large errors in computing the fair price of options. Hence, there exists a noticeable need for non-linear modelling of financial products. This book will help to foster the usage of non-linear Black-Scholes models in practice.