This review aims firstly to clarify the meanings of key terms and concepts associated with the idea of the transition state, as developed by theoreticians and applied by experimentalist, and secondly to provide an update to the meaning and significance of the transition state in an era when computational simulation, in which complexity is being increasingly incorporated, is commonly employed as a means by which to bridge the realms of theory and experiment. The relationship between the transition state and the potential-energy surface for an elementary reaction is explored, with discussion of the following terms: saddle point, minimum-energy reaction path, reaction coordinate, activated complex, transition structure, intrinsic reaction coordinate, transition vector, transition-state structure, and transition state. Structural information determined by the application of computational methods to simple systems or inferred from empirical studies is critically discussed in the light of various complications. Consequently, the relationship between the transition state and the free-energy surface for an elementary reaction within a condensed system is explored, with discussion of collective variables, minimum free-energy paths, variational transition-state theory, transmission coefficients, more about reaction coordinates, and equicommittors. It is noted that any visual picture of a transition state is necessarily an average view, and an updated definition of the transition state is proposed.