Brain tissue is an inhomogeneous, layered, multi-phase, and multi-functional material made of interconnected neural, glial, and vascular networks, and is immersed in the cerebrospinal fluid. In order to advance our understanding of how the brain provides its functions, we need to develop a robust controlled feedback engineering framework that uses fundamental science concepts to guide and interpret experiments investigating brain’s response to different types of stimuli, aging, trauma, diseases, treatment and recovery processes. Improved multi-physics constitutive models are needed that account for the complex heterogeneity and dynamics of the material brain, differentiate between healthy and diseased tissues, as well as include the mechano-chemistry regulating brain’s functions. In this context, I will present some mathematical models of brain neuro-mechanics and corresponding numerical solvers that I and my collaborators have been developing over the last decade. I will also discuss the use of fractional calculus in modeling multiple temporal scales and non-locality of brain dynamics. Lastly, I will present our generalization of the continuum mechanics theory using fractional calculus.