The 70-kDa heat shock proteins (Hsp70s) are ubiquitous molecular chaperones that act in a large variety of cellular protein folding and remodelling processes. They function virtually at all stages of the life of proteins from synthesis to degradation and are thus crucial for maintaining protein homeostasis, with direct implications for human health. A large set of co-chaperones comprising J-domain proteins and nucleotide exchange factors regulate the ATPase cycle of Hsp70s, which is allosterically coupled to substrate binding and release. Moreover, Hsp70s cooperate with other cellular chaperone systems including Hsp90, Hsp60 chaperonins, small heat shock proteins and Hsp100 AAA+ disaggregases, together constituting a dynamic and functionally versatile network for protein folding, unfolding, regulation, targeting, aggregation and disaggregation, as well as degradation. In this Review we describe recent advances that have increased our understanding of the molecular mechanisms and working principles of the Hsp70 network. This knowledge showcases how the Hsp70 chaperone system controls diverse cellular functions, and offers new opportunities for the development of chemical compounds that modulate disease-related Hsp70 activities.