In the present lecture we briefly review several methods of temporal and non-linear time series analysis, mainly based on phase space reconstruction such as recurrence plots Quadrant Scan, as well as complex network transformed time series based on the visibility algorithm. We discuss the main characteristics of the methods and the insight they can provide of the underlying physical, engineering systems as well as in other systems sch as financial time series, with special focus on system identification and transition detection, event detection, and spatial variation. We present and discuss applications from magnetohydrodynamics and turbulent flows as well as river systems and car flow incident detection financial data.