Molecular chaperones are a special class of heat shock proteins (Hsp) that assist the folding and formation of the quaternary structure of other proteins both in vivo and in vitro. However, some chaperones are complex oligomeric proteins, and one of the intriguing questions is how the chaperones fold. The representatives of the Escherichia coli chaperone system GroEL (Hsp60) and GroES (Hsp10) have been studied most intensively. GroEL consists of 14 identical subunits combined into two interacting ring-like structures of seven subunits each, while the co-chaperone GroES interacting with GroEL consists of seven identical subunits combined into a dome-like oligomeric structure. In spite of their complex quaternary structure, GroEL and GroES fold well both in vivo and in vitro. However, the specific oligomerization of GroEL subunits is dependent on ligands and external conditions. This review analyzes the literature and our own data on the study of unfolding (denaturation) and refolding (renaturation) processes of these molecular chaperones and the effect of ligands and solvent composition. Such analysis seems to be useful for understanding the folding mechanism not only of the GroEL/GroES complex, but also of other oligomeric protein complexes.