  This article contains our comments and views on the status of the current
understanding of phase transitions in systems with only hard-core interactions,
based on our work in this area. The equation of state for the hard sphere gas
in $d$-dimensions is discussed. The universal repulsive Lee-Yang singularities
in the complex activity plane, and its relation to the directed and undirected
polymer models are outlined. We also discuss orientationally disordered
crystalline mesophases, and some of their models.
