Figure-ground organization is an important early step in visual processing. It separates structured input to which processing efforts should be devoted (figure) from less structured background. Gestalt psychologists identified several variables which influence figure-ground assignment, including size, contrast, surroundness, and convexity, symmetry, parallelism and horizontal-vertical axes. Recently, several new factors affecting figure-ground organization were discovered. Those are lower region, top-bottom polarity, and extremal edges. Early neurophysiological investigations of figure-ground assignment found enhanced firing rate in the primary visual cortex of monkeys. Activity enhancement was observed in the region which corresponds to the perceived figure in texture segregation task. On the other hand, recent investigations revealed a special group of neurons in the visual cortex which detect border ownership. The figure is distinguished from the background by different responses to the same boundary. If the figure is on one side of the boundary, a certain neuron will fire, but if the figure is on the other side of the same boundary, the same neuron will be silenced and another neuron will show an enhanced firing rate. There are many computational models proposed to explain the properties of figure-ground organization. Several models focused on the boundary assignment alone. Other models are concerned with explaining psychophysical findings. Although the models share some common assumptions, there are also important differences between them. Border ownership models could not explain many of the identified Gestalt principles of figural assignment. On the other hand, psychophysical models are based on the assumptions that are not supported by the neurophysiology. Important problem for the future research is how to reconcile psychophysical and neurophysiological models in order to provide a unified account of the figure-ground organization.