The complex role played by intermediates is dissected using experimental data on apomyoglobin (apoMb), simple theoretical concepts, and simulations of kinetics of simple minimal off-lattice models. The folding of moderate-to-large-sized proteins often occurs through passage of an ensemble of intermediates. In the case of apoMb there is dominant kinetic intermediate I that also occurs at equilibrium. The cooperativity of transition of U<-->I (U represents the ensemble of unfolded states) in apoMb at pH 4.0 is determined not only by the sequence but also by the anion concentration. Point mutations can substantially alter the cooperativity of formation of I. Another class of intermediates arise owing to bottlenecks in the rugged energy landscape that arises from topological frustration. As a result of the rough energy landscape, folding is predicted to follow the kinetic partitioning mechanism (KPM). According to KPM a fraction of molecules reaches the native state rapidly, while the remaining fraction is kinetically trapped in intermediates. The folding of lysozyme at pH 5.5 follows KPM. Our perspective also shows that the fraction of fast folding trajectories can be altered by changing pH, for example. These observations are clearly illustrated in simple off-lattice models of proteins. The simulations show that equilibrium intermediates occur "on-pathway" and have substantial probability to be revisited after the native state is reached, while kinetic intermediates are almost never sampled after native state is reached. In addition, kinetic intermediates are higher in free energy than equilibrium intermediates. We also discuss the consequences of multiple routes and intermediates on the transition state ensemble (TSE) in folding. Whenever multiple routes to the native state dominate, Phi-values can be larger than unity or less than zero. There appears to be a relationship between the diversity of structures in the denatured state ensemble and the extent to which the TSE is plastic. Simulations of beta-hairpins are used to illustrate these ideas.