Theory and methodology from nonlinear dynamical systems (NDS) may provide considerable advantage to health scientists as well as health care professionals. For instance, NDS methodologies and topics in health care share a focus upon the potentially complex interactions of biological, psychological and social factors over time. Nevertheless, a number of challenges remain in creating the necessary bridges in understanding to allow researchers to apply NDS techniques and to enable practitioners to use the resulting evidence to improve patient care. This article aims to provide such a bridge. First, common concepts pertaining to self-organizing complex adaptive systems are outlined as a general approach to understanding resilience across biological, psychological, and social scales. Next, four data analytic techniques from NDS are compared and contrasted with respect to the information they may provide about some common processes underlying resilience. These techniques are: time-series analysis, state-space grids, catastrophe modeling, and network modeling. Implications for health scientists and practitioners are discussed.