Tipping points in the scientific literature are characterized by a sudden, qualitative shift in the behavior or state of the system due to a relatively small change in inputs. In mathematical models, tipping can be caused bifurcations, noise, and rapid shifts in parameters even in the absence of these other two mechanisms. In this talk I'll give a broad overview of mathematical tipping points and some applications in conceptual climate models. I'll then give a closer look at rate-dependent tipping in 1D systems and the methods that I'm working on in a project here at Cornell.