When available, the data on incubation periods, i.e., times between the exposure to an infection and the onset of symptoms, exhibit striking universal features over a range of diseases and associated time scales. In this talk, I will show how these features such as right-skewness and more detailed distributional properties can be explained with the help of models based on diffusion processes. I will also have time to talk about applications of similar models to reaction/decision times in psychology, about limitations of such modeling, and about the problem of universality of stopping/halting times in decision making /computing in general.