Within the framework of the mode-coupling theory of super-cooled liquids, we investigate new phenomena in colloidal systems on approach to their glass transitions. When the inter-particle potential contains an attractive part, besides the usual repulsive hard core, two intersecting liquid-glass transition lines appear, one of which extends to low densities, while the other one, at high densities, shows a re-entrant behaviour. In the glassy region a new type of transition appears between two different types of glasses. The complex phenomenology can be described in terms of higher order glass transition singularities. The various glass phases are characterized by means of their viscoelastic properties. The glass driven by attractions has been associated with particle gels, and the other glass is the well known repulsive colloidal glass. These correspondences, in association with the new predictions of glassy behaviour, mean that such phenomena may be expected in colloidal systems with, for example, strong depletion or other short-ranged attractive potentials.