Complicated models, for which a detailed analysis is too far out of reach, are routinely approximated via a variety of procedures, for example by use of numerical schemes. When using a numerical scheme we make an error which is small over small time-intervals but it typically compounds over longer time-horizons. Hence, in general, the approximation error grows in time so that the results of our simulations are less reliable when the simulation is run for longer. However this is not necessarily the case and one may be able to find dynamics and corresponding approximation procedures for which the error remains bounded, uniformly in time. We will discuss some criteria and approaches to understand when this is possible. We will start by considering the simple case of approximations produced via the Euler scheme and then, time allowing, consider more general approximation procedures, i.e. averaging.