There is common ground in analysing the health state of human beings and the state of ecosystems, especially in the need to identify conditions that dispose a system to be knocked from seeming stability into another, undesired state. In ecology, relatively simple system dynamics models have proven to be valuable to understand such dynamics. Examples include lakes that unexpectedly shift from a clear to a turbid state, or coral reefs that are suddenly overgrown by macroalgae. In this talk, I will introduce you to the world of dynamical models, and provide examples how they have proven their value in ecology. Based on that, I will discuss assumptions, benefits and limitations. Then, I will explain how the analysis of bifurcations has led to the development of Dynamic Indicators of Resilience (DIORs). Finally, I will make a bridge from ecology to health, and point to some open questions in relation to DIORs, networks, and oscillating dynamics.