Weather, climate, earthquake and forex are a few examples of a vast list of complex real world dynamical systems where forecast of extreme events that would occur in future is of great value. Accurate prediction of such events requires a critical understanding of the dynamics of these complex systems. The introduction of nonlinear time series analysis has given significant insights into the temporal patterns in the dynamics of the aforementioned systems. There are many nonlinear analysis methods proposed for analyzing a given time series including, but not limited to, fluctuation analysis, synchronization, entropy and recurrence analysis. In the present talk, I will be discussing some of the aforementioned techniques which were used by us for analysis of biological and physical systems.