Anticipating abrupt changes in ecosystem state is key for ecosystem management and preservation. Detailed knowledge of ecological mechanisms behind a critical transition is often difficult to attain, and the theory of resilience – assessment of the ability of a system to withstand disturbances – provides a pathway to circumvent this problem. Loss of system resilience is referred to as critical slowing down if the system is gradually approaching a tipping point. Critical slowing down can be detected using summary statistics, called early warning indicators. Here, we illustrate the theory with a series of models that both represent fundamental ecological ideas (e.g., density-dependence) and are amenable to mathematical analysis. These analyses provide theoretical predictions about the nature of measurable fluctuations in the vicinity of a tipping point. Next, we introduce a novel early warning signal of an impending critical transition called reactivity, which characterizes the amplification of an initial response of a system to a disturbance. We show that reactivity increases prior to elimination and emergence in infectious disease systems. We test the performance of reactivity using epidemic models approaching elimination and emergence through a simulation study. The results of the simulation study indicate that predictions for reactivity patterns are robust. Finally, we discuss advantages and limitations of early warning indicators based on critical slowing down, and how a mathematical foundation is necessary to draw conclusions from summary statistics obtained from a system near a tipping point.