This article reviews recent advances in understanding amorphous glassy states in dense colloidal suspensions with or without short-range interparticle attractions. Experiments, theory, and simulation show that two kinds of glassy states are possible, dominated respectively by repulsion and attraction. Under suitable conditions, a small change in the interparticle potential can lead to a transition between these two kinds of colloidal glasses that entails sharp changes in material properties such as the shear modulus. This may provide novel routes for fine-tuning the properties of industrial pastes and slurries.