Organisms and other biological entities are mistake-prone: they get things wrong. The entities of pure physics, such as atoms and inorganic molecules, do not make mistakes: they do what they do according to physical law, with no room for error except on the part of the physicist or their theory. We set out a novel framework for understanding biology and its demarcation from physics – that of mistake-making. We distinguish biological mistakes from mere failures. We then propose a rigorous definition of mistakes that, although invoking the concept of function, is compatible with various views about what functions are. The definition of mistake-making is agential, since mistakes do not just happen – at least in the sense analysed here – but are made. This requires, then, a notion of biological agency which we set out as a definition of the Minimal Biological Agent. The paper then considers a series of objections to the theory presented here, along with our replies. Two key features of our theory of mistakes are, first, that it is a supplement to, not a replacement for, existing general frameworks within which biology is understood and practised. Secondly, it is designed to be experimentally productive. Hence we end with a series of case studies where mistake theory can be shown to be useful in the potential generation of novel hypotheses of interest to the working biologist.