The nature of dark matter is one of the most important outstanding problems in physics and cosmology. From observing astrophysical objects, we have learned that dark matter represents some 25% of the total energy of the universe, while ordinary matter weighs in at only about 4%. Although they make up a large fraction of the energy of the universe, dark matter particles interact with ordinary matter only very weakly, making their detection via interactions with ordinary matter difficult. We examine some of the constraints and cosmic clues for the nature of the dark matter, and consider some of the recent possible signals for its direct detection. These clues and constraints provide the basis for examining in greater detail a previously little explored class of models, where the dark matter carries a conserved global charge analogous to baryon number. We discuss a few explicit models, and examine their implications, including a few technical aspects of the evolution of the dark matter density and their connections to astrophysical objects such as neutron stars.