In the traditional conception of science one assumes that science produces results which are certain and precise. It is argued that this picture is flawed and needs to be replaced with a view where uncertainty and imprecision are an integral part of the scientific enterprise. Uncertainty is still poorly understood by many practising scientists. However, several developments in science indicate that some epistemological uncertainty, e.g. due to processes of abstraction and idealization, will always follow advances in scientific knowledge. There are (...) also other developments that indicate some principal ontological uncertainties, i.e. uncertainties that are due to how the world is. Complexity is one such example. Remarks on post-normal science are thus included. This paper argues, therefore, that scientific uncertainty is a multi-dimensional concept, and that it is unavoidable because it is often the result as much as the cause of new knowledge. (shrink)