The Standard Model of particle physics (SM) is a theoretical framework that integrates our current knowledge of the subatomic world and its fundamental interactions. A key program built in the structure of the SM is the Renormalization Group (RG), whose function is to preserve self-consistency and describe how parameters of the theory evolve with the energy scale. Despite being overwhelmingly supported by experimental data, the SM has many puzzling aspects, such as the large number of parameters, a triplication of chiral families and the existence of three gauge interactions. In contrast with the majority of mainstream proposals advanced over the years, the basic premise of our study is that a satisfactory resolution of challenges confronting the SM requires further advancing the RG program. In particular, understanding the nonlinear dynamics of RG equations and the unavoidable transition from smooth to fractal dimensionality of space-time are critically important for the success of this endeavor. Here we show how the onset of fractal space-time near or above the electroweak scale is likely to settle at least some of these challenges.