Qualitatively, a tipping point in a dynamical system is when a small change in system inputs causes the system to move to a drastically different state. The discussion of tipping points in climate and related fields has become increasingly urgent as scientists are concerned that different aspects of Earth’s climate could tip to a qualitatively different state without sufficient warning (e.g., loss of summer sea ice in the Arctic).  Often a system that has tipped is difficult or even impossible to return to its original state, making the study of predicting and preventing tipping phenomena extremely important. In this talk, I will overview three main mathematical causes for tipping in dynamical systems as well as examples of each in different climate models. I will discuss the recent endeavors to put one of these causes—rate-induced tipping—on firm mathematical footing.  I will show how viewing this type of tipping from a nonautonomous framework allows us to extend the types of systems we can analyze for tipping phenomena.