What on earth is a ray and how can we use them best?

Although rays form the basis of both our intuitive thinking and our numerical modelling of optical systems, we must remember that they are no more than mathematical constructs with a relatively tenuous connection to the physical world. What's more, certain aspects of their link to wave-based models of optical systems have always been problematic. For example, the limit to what rays can tell us about the associated wave field remains unclear. The current state of the art is reviewed and a framework is then outlined that offers a more direct appreciation of these issues and promises extended capabilities for ray-based methods. The new approach involves modelling wave propagation by using - as an intermediate tool - a windowed Fourier transform of the field.