This special issue of Complexity initially aimed at gathering leading-edge up-to-date studies showcasing the occurrence of fractal features in the dynamics of highly nonlinear complex systems. More than thirty years after coining term by Mandelbrot [1], fractals continue to fascinate the scientific community or the general public, with their wonderful propensity to infinitely repeat the same patterns at various (spatial and/or temporal) scales. On a more specialized ground, these continuous but nondifferentiable mathematical objects have become increasingly useful tools in developing original approaches to efficiently model natural or physical phenomena which escape from the traditional horizon of Euclidean metrics. Their range of applications is tremendously wide, from the well-known initial quest of measuring the length of Britain coast [2] to the most recent investigations on digital image processing for materials science [3], chaotic circuits [4], information technology [5], and medicine [6]. Initially developed at macro/mesoscopic scales, these objects penetrate now the nanoworld [7] with the development of ultrahigh resolution probes. At a temporal level, modeling of ultrafast phenomena (as peculiar oscillations evidenced in transient laser-generated plasmas [8]) can benefit from innovative scale relativity of fractal-based theoretical developments [9].Although appealing, the initial fractal-oriented scope of this special issue has been proven to be quite sharp, and the decision was taken, in agreement with the journal editorial board, to broaden its range to a more general nonlinear dynamic field. In this context, 17 papers have been received for review, covering a wide variety of topics, from "pure" mathematics and theoretical physics to applications in materials science, plasma physics, medicine, and financial markets. Despite the high quality of all submitted papers, the very rigorous review process retained only seven of them for publications in this special issue. A brief presentation of each accepted paper is given in the following.In "Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations," N. Ahmad et al. use a powerful combination of Caputo fractional derivatives and classical fixed point theorems (Banach and Krasnoselskii) to investigate the existence, uniqueness, and various kinds of Ulam-Hyers stability [10] of the solutions to impulsive fractional differential equations with nonlocal boundary conditions. A "pure" mathematical object, the Ulam concept of stability [10], finds quite significant applications in real-world problems like the formation of rogue waves (tsunami) in the oceans or the design of ultrahigh precision optical clocks. A very recent example is offered by the observation in optical fibers of the broken symmetry of Fermi-Pasta-Ulam recurrence [11]. In another "mathematical" paper of this special issue ("Moderate Deviations for Stochastic Fractional Heat Equation Driven by Fractional Noise"), X. Sun et al. use a fractional Laplacian ...