How do we choose one option rather than another when faced with uncertainty about the information we receive, and the consequences of what we decide? The LATER (Linear Approach to Threshold with Ergodic Rate) model has proved to be remarkably accurate in predicting how we respond in such situations. Given its conceptual simplicity, its grounding in fundamental Bayesian principles and its very few free parameters, it is being increasingly adopted for a wider range of choice tasks, helping us to understand the underlying neural mechanisms, and in applying this to clinical disorders. Here, we provide a thorough discussion of the history behind this model, and how it can be applied to more complex decisions, including anti-saccades, Go-NoGo, countermanding and other situations where newly-arriving information means that ongoing decisions must be modified. The neuroscience of decision-making is progressing rapidly, and we anticipate that wider understanding and application of this model will help simplify the interpretation of increasingly advanced decision behaviour both in the laboratory and clinic.