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The leaky competing accumulator (LCA) is a biologically inspired model of choice. It describes the processes of leaky accumulation and competition observed in neuronal populations during choice tasks and it accounts for reaction time distributions observed in psychophysical experiments. This paper discusses recent analyses and extensions of the LCA model. First, it reviews the dynamics and examines the conditions that make the model achieve optimal performance. Second, it shows that nonlinearities of the type present in biological neurons improve performance when the number of choice alternatives increases. Third, the model is extended to value-based choice, where it is shown that nonlinearities in the value function explain risk aversion in risky choice and preference reversals in choice between alternatives characterized across multiple dimensions.