Biochemical activity and core stability are essential properties of proteins, maintained usually by conserved amino acids. Structural dynamics emerged in recent years as another essential aspect of protein functionality, which enables the adaptation of the protein to substrate binding. It also underlies its ability to undergo allosteric transitions, while maintaining its fold. Key residues that mediate structural dynamics would thus be expected to be conserved, or exhibit co-evolutionary patterns at least. Yet, the correlation between sequence evolution and structural dynamics is yet to be established. To this end, we have performed in-depth analyses of a number of representative proteins, using a combined approach of sequence analyses and coarse-grained physics-based models. For the Hsp70 family, we studied the interactions of Hsp70 ATPase domains with four different nucleotide exchange factors (NEFs) and revealed two classes of key residues: (i) those highly conserved residues involved in nucleotide binding, which mediate the ATPase domain opening via a global hinge-bending, and (ii) those co-evolving and highly mobile residues engaged in specific interactions with NEFs. The observed interplay between these respective intrinsic (pre-existing, structure-encoded) and specific (co-evolved, sequence-dependent) interactions provides us with insights into the allosteric dynamics and functional evolution of the modular Hsp70 ATPase domain, and inspired a follow-up study that identified a group of key residues mediating the Hsp70 allosteric pathways using perturbation analysis. Along the same lines, a systematic study has been performed on a set of 34 enzymes representing various folds and functional classes, which generalizes the previous findings and unravels a unique correlation between sequence evolutionary properties and conformational dynamics. Our findings suggest that there is a balance between physical adaptability (enabled by structure-encoded motions) and chemical specificity (conferred by correlated amino acid substitutions), and this balance underlies the selection of a relatively small set of versatile folds by proteins. In another study, HIV-1 protease was investigated as a special case in which short-term evolutionary pressure plays a significant role. With advanced clustering techniques, we differentiated multi-drug resistant mutations from those arising from phylogenetic variations; correspondingly, these mutations exhibit distinctive structural/dynamical features, underlying the role of protein dynamics in conferring drug resistance.