In this non-technical talk, we discuss uncertainty – why it needs to be modelled – the role of probability theory, brief history of probability, and some of its popular applications. We focus especially on modelling tail events - events that occur with small probability but can lead to catastrophic consequences. For last two centuries, many natural and social phenomenon were thought to follow the light-tailed Normal distribution or the `Bell Curve’. Lately, particularly in social settings, one sees fat-tailed distributions. In this talk, we also shed light on the underlying principles governing these distributions.