The Hierarchical Continuous-Time Random Flight (HCTRF) formalism enhances our understanding of anomalous transport and diffusion phenomena, particularly in amorphous and vitreous solids and conducting light-emitting organic polymers. This formalism is grounded in the canonical random trap or valley model, in which the disorder of the energy landscape is characterized by an exponential distribution. The corresponding mean residence times within the traps exhibit power-law behavior. This disorder pattern is typical of various amorphous materials, including those with commercial applications, which renders the HCTRF formalism highly applicable. Furthermore, by leveraging Extreme Value Theory (EVT), we demonstrate that rare or extreme stochastic events significantly influence the transport and diffusion processes of these materials. This chapter employs a hierarchical waiting-time distribution and investigates biased HCTRF on a regular lattice with random depth traps. We integrate this model with statistical EVT and the Weierstrass random walk framework. The HCTRF can be seen as a variant of the Continuous-Time Random Walk (CTRW) formalism [1–4], encompassing both random walks and flights.