Choice models in marketing and economics are generally derived without specifying the underlying cognitive process of decision making. This approach has been successfully used to predict choice behavior. However, it has not much to say about such aspects of decision making as deliberation, attention, conflict, and cognitive limitations and how these influence choices. In contrast, sequential sampling models developed in cognitive psychology explain observed choices based on assumptions about cognitive processes that return the observed choice as the terminal state. We illustrate three advantages of this perspective. First, making explicit assumptions about underlying cognitive processes results in measures of deliberation, attention, conflict, and cognitive limitation. Second, the mathematical representations of underlying cognitive processes imply well documented departures from Luce’s Choice Axiom such as the similarity, compromise, and attraction effects. Third, the process perspective predicts response time and thus allows for inference based on observed choices and response times. Finally, we briefly discuss the relationship between these cognitive models and rules for statistically optimal decisions in sequential designs.