We present both the consequences of scaling symmetry and those of the Generalized Central Limit Theorem, including applications that describe selected elements of the dynamics of financial markets, such as log-periodicity. Additionally, in the context of viscoelastic materials (e.g., non-Newtonian fluids), we explore the phenomenon of slowed (or non-Debye) relaxation. In this context, we introduce the concept of fractal relaxation and the corresponding evolution equation with memory effects. However, the key element of this chapter is anomalous diffusion: we address its definition, the most commonly employed probability density functions (PDFs) leading to anomalous diffusion, and the introduction of singular processes as a generalization of this phenomenon. This framework lays the foundation for defining the conditions necessary to emerge multifractal stochastic processes—a broad category of singular stochastic processes. We discuss the stochastic process known as normal fractional Brownian motion and its generalization, fractional Brownian motion. We emphasize one of the most important properties of singular processes: long-range (and/or long-term) autocorrelations. Furthermore, we relate this type of process to the Langevin equation of stochastic dynamics, which we treat here at an ab initio level. At the end of this chapter, we discuss the monofractal subdiffusion process as a reference case.