The importance of flexibility and stability on protein function has been recognized for over five decades. A protein must be flexible enough to mediate a reaction pathway, yet rigid enough to achieve high fidelity in molecular recognition. To understand these relationships, the main focus of our research has been a comparative investigation of proteins' dynamics and thermodynamics across both "depth" and "breadth". Specifically, we compare stability and flexibility properties across a set of human c-type lysozyme point mutations (depth), as well as across a set of functionally related β-lactamase protein orthologs (breadth). To accomplish these tasks we employ a Distance Constraint Model (DCM), which provides a robust statistical mechanical description of proteins and the relationships therein. The DCM is based on network rigidity that provides mechanical mechanism for enthalpy-entropy compensation, from which Quantitative Stability/Flexibility Relationships (QSFR) can be calculated. Our results suggest that DCM can be used for predicting stability of proteins with an average percent error of 4.3%. Deciphering changes in flexibility, DCM results suggest that the influence of mutations can lead to frequent, large and long-range effects in protein dynamics. Our breadth analyses indicate that QSFR and physiochemical property characterization of orthologs in a protein family parallel evolutionary relationship. Going further, we present protocols for clustering protein structures using their QSFR properties, thus paving way for comprehensive quantitative stability/flexibility relationship analysis across protein families and superfamilies. To summarize, the results presented in this work provide a complete description of proteins that account for their stability, flexibility and function.