Animals are intrinsically computational. We acquire sensory information about our environments, transform this information into neural representations and memories, and calculate and execute decisions based on recent and past experiences. Our own brains are staggeringly complex, with billions of neurons networked by trillions of synapses. But the basic "stuff" of our brains -- molecular and cellular structures and interactions -- is shared with our simplest animal relatives. Thus simple and well-chosen model organisms can be accessible vantage points with perspective over general biological principles. We study brain and behavior in the roundworm C. elegans. The worm only has 302 neurons, but is capable of a variety of behaviors that display a range of computational powers. We focus specifically on navigational behaviors responding to physical sensory inputs. These inputs (e.g., temperature, pressure, electric fields) can be delivered to the behaving worm both reliably and quantifiably. Navigation itself can be reduced to a quantified pattern as an alternating sequence of forward movements, turns, and reversals. From the systematic analysis of outward motile behavior we can infer the inner workings of neural algorithms. Applying recent advances in microscopy and optics, we are also able to manipulate and monitor the workings of these neural circuits in the intact animal. In this way, we strive to link brain and behavior in the simple but fascinating creature.