NMR is a vital tool for measuring the dynamics of biological macromolecules in solution. The chemical exchange observed is often divided into slow or intermediate exchange. Slow exchange affects principally the z magnetizations of the system, and is observed in modified spin-lattice relaxation experiments. Intermediate exchange gives rise to broadening and coalescence in the spectrum itself. This broadened spectrum is often considered as a whole, but we have shown that it is better to regard it as a sum of transitions, with a generalized picture of the transition probability. In this paper, we give explicit expressions for the lineshape for two sites, and review some of the recent applications of chemical exchange in biochemical NMR.