Depending on the pair interactions of the constitutive system particles, colloidal dispersions display a rich phase behaviour. An important class of colloidal systems is characterised by pair potentials that contain a hard core in addition to versatile potential tails. This class of systems are investigated, focussing on two different aspects. The first one is represented by the critical behaviour of long-range interaction systems. With proper ameliorations of state-of-the-art techniques it is possible to find a cross-over in the critical behaviour of various models, and a new relation for the ascertainment of the critical exponent describing the divergence of the isothermal compressibility at the critical point is verified. The second focus is laid on the search for solid equilibrium structures of hard core systems, for which we employ a search strategy based on a genetic algorithm. The astonishingly large variety of the identified equilibrium structures for the square-shoulder model consist of cluster, columnar, lamellar, and compact phases - explicable by the continuum theory. In addition the existence of a new centred tetragonal phase for the hard core Yukawa model is revealed.