I will introduce some basic concepts and methods from nonlinear time series analysis and discuss applications that may hold implications for a diverse body of scientific groups: from scientists who study physical ocean processes such as El Nio events to environmental managers charged with overseeing and sustaining ecosystem resources such as fisheries. Of particular interest is the fact that the concepts and methods relate to many disciplines involving complex webs of mutually interacting parts, such as ecosystems and world financial markets, which have the potential for unexpected collapse and irreversible change.