Tracy-Widom law was first discovered by two mathematicians Tracy and Widom in the study of eigenvalues high dimensional random matrices in the nighties. There have been a lot of intensive research activities around this law in the past 25 years. It turns out that Tracy-Widom law have a universality property in describing the extremal random phenomena as normal law in the cumulative sum phenomena. Besides, a new type of processes, so-called Airy Processes, have also be introduced through finite dimensional marginal distributions related to Tracy-Widom law recently. Unlike Gaussian processes, there is little research work on the sample path properties for Airy Processes, but this will no doubt be the next important and challenging subject of study in this area.

In this talk I will briefly review some basic concepts and advances about Tracy-Widom law and Airy processes from my personal viewpoint and taste.