Humans and animals are constantly facing the problem of having to choose from a variety of possible actions as they interact with the environment. Both external and internal cues have to be used to guide their selection of a single action from many possible alternatives. Which action to choose in a given context may have important biological consequences to their survival. Decision making is regarded as an accumulation process of evidence about the state of the world and the utility of possible outcomes. Two well established neural accumulator models of decision making are presented to model the neural basis of decision making in behavioural paradigms such as the antisaccade task.