Extreme events such as cyclones, earthquakes, power blackouts or traffic jams are not uncommon. Study of such events using the framework of extreme value theory has a long history. In this talk, we will introduce the idea of extreme events and review some of the recent results. In the second half, we will discuss transport processes based on random walks and associated extreme events taking place on complex networks. We show that extreme events on complex networks are more likely to take place on small degree nodes and not on the hubs. We will discuss some generalisations and applications of these results.