Exponential integrators are a special class of numerical integration methods for stiff initial value problems. They are based on the exact integration of a linear approximation of the vector field; the remainder is then adequately accounted for by the variation of constants formula. The idea of exponential integrators can be traced back to the late 1950s. Its development proceeded in several steps and was always closely related to the possibility of efficiently computing the action of the exponential and related matrix functions. This task is by no means independent of the approximation chosen for the vector field. In my talk I will give a brief overview of the developments so far and discuss some current research questions.
