The provision of advice on animal welfare is an important part of the work of scientists in applied ethology, neurophysiology, veterinary epidemiology and other disciplines. Those who request guidance often expect advice that will help them to make progress in difficult discussions. Scientists want to live up to these expectations, but it is also important for them to clarify any scientific limitations. They are normally aware of limits to their advice, but these limits are sometimes not explicitly stated. Using the phrase broadly, we call this kind of limitation ‘scientific uncertainty’. We distinguish between the following four types of uncertainty: I) Ontological uncertainty, relating to the existence of animal feelings and other states relevant for animal welfare. 2) Conceptual uncertainty, stemming from the fact that some of the concepts used in animal welfare science are value-laden if used outside a narrow scientific context. 3) Lack of scientific evidence, stemming from a lack of scientific data on the problem in question. 4) Uncertainty about priorities, relating to the practical conclusions to be drawn in a situation with an open-ended set of ethical and other practical considerations. Scientific uncertainty is unavoidable. It is therefore essential, when giving scientific advice, to state the assumptions on which the advice is based. This makes scientific advice more objective, but also of more limited value to those who do not share the underlying assumptions.