In contrast to linear time-series analysis which is a fairly established area, nonlinear time-series analysis still requires the proposal of new models and development of new methodologies. Forgetting about linearity and the Gaussian assumption requires new ways of conceiving the statistical methodology. This translates to the development of data-driven (nonparametric) approaches to regression and estimation, data transformation aspects, new correlation concepts, etc. These new statistical modeling techniques are then applied to a wide range of practical problems, for which they prove their superiority in terms of model fitting, resulting forecast accuracy, and in their ability to explain the underlying processes.