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Recent advances in DNA sequencing technologies led to the accumulation of enormous quantities of genetic information available in public databases. This rapid growth of available biological datasets calls for quantitative analysis tools and concomitantly opens the doors for new analysis paradigms. Particularly, the analysis of correlated mutations and their structural interpretation have witnessed a second youth in the last years. A natural formulation for such approaches is provided by the statistical physics of disordered systems. This thesis is articulated around different projects aimed at studying particular biological systems of interests, the Hsp70 molecular chaperones, through the lens provided by methods rooted in statistical physics. In a first project, we focus on correlated mutations within the Hsp70 family. Our analysis reveals the existence of a biologically important macro-molecular arrangement of these chaperones and we investigate its phylogenetic origin. A second project investigates the interactions between the Hsp70 chaperones and one of their main co-chaperones, J-proteins. Through the combined use of coevolutionary analysis and molecular simulations at both coarse-grained and atomistic levels, we construct a structural and dynamical model of this interaction which rationalizes previous experimental evidence. In a subsequent study, we specifically focus on the J-protein co-chaperones. Through phylogenetic and coevolutionary methods, we investigate the origin of recently discovered interactions which form the basis of the disaggregation machinery in higher eukaryotes. Finally, in a fourth project, we shift our attention to the analysis of proteins involved in the iron-sulfur cluster assembly pathway. Analysis of residue coevolution in the different proteins composing this pathway reveals multiple structural insights at several scales.