Mechanisms and kinetics of protein folding in living cells differ substantially from that occurring in vitro. These differences are associated with molecular chaperones, which are the proteins helping other proteins to fold into native structures. Some of the chaperones are ATPases which are activated by folding protein substrates. Possible mechanisms of chaperone assistance of protein folding and its coupling with ATPase reaction will be discussed. For chaperoned protein folding we will discuss the validity of principle of self-assembly, solution of Levinthal paradox, the role of folding steps and itermediates, the issue of microscopic reversibility. The results on biophysical modeling are analyzed in most detail. It is of general value to understand how the stochastic event of spontaneous folding can be put under spatial and temporal control by cellular factors.