Natural systems are often complex and highly nonlinear, making them difficult to understand using linear statistical approaches, such as correlation. However, these linear approaches are ill-posed for dynamical systems, where correlation can occur without causation, and causation may also occur in the absence of correlation.“Mirage correlation” (i.e. the sign and magnitude of the correlation change with time) is a hallmark of nonlinear systems that results from state dependency that the relationships among interacting variables change with different states of the system. In recent decades, nonlinear methods that acknowledge state dependence have been developed rooted in Takens theorem using state space reconstruction, i.e. lagged coordinate embedding of time series data. Because there is no assumption on equations governing dynamical systems, it often refers to empirical dynamic modelling (EDM). Several important applications and novel development of algorithms will be introduced.