Proteins are the machines of living systems that carry out a diverse set of essential biochemical functions. Furthermore, the diversity of their functions has grown overtime via molecular evolution. This thesis aims to explore fundamental questions in protein science regarding the mechanisms of protein evolution particularly addressing how substitutions in sequence modulate function through structure and structural dynamics. In the work presented here, the first goal is to develop a set of tools which connect the sequence-structure relationship which are implemented in two major projects of protein structural refinement and protein structural design. Both of these two works highlight the importance of capturing important pairwise interactions within a given protein system.The second major goal of this work is to understand how sequence and structural dynamics give rise to protein function, and, importantly, how Nature can utilize allostery to evolve towards a new function. Here I employ several in-house and novel computational tools to shed light onto the mechanisms of allostery, and, particularly dynamic allostery in the absence of structural rearrangements. This analysis is applied to several different protein systems including Pin1, LacI, CoV-1 and CoV-2 and TEM-1. I show that the dynamics of protein systems may be altered fundamentally by distal perturbations such as ligand binding or point mutations. These peturbations lead to change in local interactions which cascade within the 3-D network of interaction of a protein and give rise to flexibility changes of distal sites, particularly those of functional/active residues positions thereby altering the protein function. This networking picture of the protein is further explored through asymmetric dynamic coupling which shows to be a marker of allosteric interactions between distal residue pairs. Within the networking picture, the concept of sequence context dependence upon mutation becomes critical in understanding the functional outcome of these mutations. Here I design a computational tool, EpiScore, which is able to capture these effects and correlate them to measured experimental epistasis in two protein systems, dihydrofolate reductase (DHFR) and TEM-1. Ultimately, the work provided in this thesis shows that both allostery and epistasis may be considered, and accurately modeled, as intrinsic properties of anisotropic networks.