The dynamics of chemical reactions are often governed by transient species, including the transition state for activated bimolecular reactions. Such transient species are difficult to study experimentally, but it has proven valuable to prepare and probe transition-state dynamics by the photodetachment of anions with an equilibrium geometry similar to the neutral transition state. In this review, recent experimental advances in photoelectron and photoelectron-photofragment coincidence spectroscopy are discussed, as well as the latest progress in the calculation of multidimensional potential energy surfaces and quantum dynamics calculations that have enabled an extension of studies of transition-state dynamics to increasingly multidimensional polyatomic systems. Examples of important dynamical effects such as mode specificity, tunneling, resonance and product energy disposal in reaction dynamics are discussed.