In the face of global biodiversity declines, predicting the fate of biological systems is a key goal in ecology. One popular approach is the search for early warning signals (EWSs) based on alternative stable states theory. In this review, we cover the theory behind nonlinearity in dynamic systems and techniques to detect the loss of resilience that can indicate state transitions. We describe the research done on generic abundance‐based signals of instability that are derived from the phenomenon of critical slowing down, which represent the genesis of EWSs research. We highlight some of the issues facing the detection of such signals in biological systems – which are inherently complex and show low signal‐to‐noise ratios. We then document research on alternative signals of instability, including measuring shifts in spatial autocorrelation and trait dynamics, and discuss potential future directions for EWSs research based on detailed demographic and phenotypic data. We set EWSs research in the greater field of predictive ecology and weigh up the costs and benefits of simplicity vs. complexity in predictive models, and how the available data should steer the development of future methods. Finally, we identify some key unanswered questions that, if solved, could improve the applicability of these methods.