Approaches to reinforcement learning and statistical decision theory from artificial intelligence offer appealing frameworks for understanding how biological brains solve decision problems in the natural world. In particular, these engineering approaches typically begin with a clear, normative analysis of the optimal solution to the problem. However, rather than stopping there, they focus on realizing it, often approximately, with a step-by-step algorithmic solution, which lends itself naturally to process-level accounts of the psychological and neural mechanisms underlying behavior and its suboptimalities. In this tutorial I will review research into biological decision making and reinforcement learning from psychology, ethology, behavioral economics, and neuroscience. I will focus on how the brain may implement different approximations to the ideal observer, how this may help to explain notions of modularity or multiplicity of decision systems across several domains, how these approximations might be understood as boundedly rational when taking into account the costs and benefits of computation, and how these mechanisms might be implicated in self control and psychiatric disorders.