The central values and typical fluctuations are insufficient to fully characterize natural systems that exhibit rare but extreme events, which can often dominate the long-term behavior of time series generated by various random walks. Consequently, the statistics of extrema represent a classical subject of significant interest in mathematics, physics, and the social and economic sciences [1–5]. In physics, extreme events have been extensively studied across multiple disciplines [6] (and references therein), including self-organized fluctuations, critical phenomena, material fracture, disordered systems, and turbulence. Understanding the statistics of extreme events is fundamentally important for predicting and assessing risks associated with various natural and man-made phenomena, such as earthquakes, climate change, floods, and substantial movements in financial markets. A relatively new area where extreme statistics has gained attention is complex networks [6]. In this chapter, we present the key aspects of Extreme Value Theory (EVT) articulated by physicists. This framework facilitates the direct application of EVT in the analysis of risk and random walks in amorphous materials.