It is known that the equations of viscous, compressible flow admit solutions in which vacuum states occur, that some of these solutions are not physical, and that uniqueness and continuous dependence on initial data fail in general. I will review these issues and will propose a simple reformulation of the definition of weak solution which is tailored to avoid these difficulties, and then will present a result proving the existence of weak solutions in the proposed sense. Both the physics and the mathematics are fairly elementary, so the talk should be widely accessible.