This project deals with the construction and analysis of algorithms for the approximation of the solution of stochastic evolution equations. Such equations are used for modelling in, e.g., population genetics, chemical reaction kinetics and finance. Emphasis lies on finding algorithms that optimally relate the error and the computational cost. For proving optimality we establish lower bounds of the form: The error of any algorithm with cost N is at least e(N ). Here, the quantity e(N ) does not depend on the algorithm but only on the evolution equation under consideration. An almost optimal algorithm achieves an error close to e(N ) with cost N . The construction of such algorithms is based on non-uniform time discretizations. Simulation experiments complement the theoretical analysis.