In this review, an overview of itinerant magnets without magnetic elements is presented, beginning with a comparison of the local and itinerant moment pictures, the two extremes of magnetism. Then, the theoretical developments leading up to the self-consistent renormalization theory of spin fluctuations will be discussed, followed by an introduction to quantum criticality and the experimental signatures associated with systems near a quantum critical point. Three itinerant magnets without magnetic elements, ZrZn, ScIn, and TiAu are the focus of this review, as their empty d shells set them apart in their purely itinerant character, while several enhanced Pauli paramagnets and intermediate moment magnets are also discussed to put the overall comparison into perspective.