The origin of magnetism in metals has been traditionally discussed in two diametrically opposite limits: itinerant and local. Itinerant magnetism, caused by conduction electrons, has been of interest due to intriguing phenomena that frequently accompany it: heavy fermion behavior, coexistence of superconductivity and magnetism, metamagnetic transitions, spin- and cluster-glass behavior, multisublattice magnetism, non-Fermi liquid behavior, and quantum criticality. Surprisingly, while many systems exhibit both local and itinerant magnetism, only two are known to contain no local moment ions: Sc3In and ZrZn2. Doping experiments on Sc3In were used to investigate the effects of both magnetic (Er) and non-magnetic (Lu) substitutions within the itinerant matrix. While the former induces a cluster-glass state, the latter drives the system through a quantum phase transition. A novel Arrott-Noakes scaling indicates that Sc3In cannot be described by the mean-field theory, contrary to what has been seen in ZrZn2. This indicates that ZrZn2 and Sc3In are drastically different, which is likely associated with the dimensionality of spin fluctuations. Given these disparities between two seemingly analogues systems, more itinerant compounds containing non-magnetic elements are needed. While the Stoner criterion for band ferromagnetism calls for high density of states at the Fermi level together with strong electron correlations, more conditions are likely at play. A systematic search among 3d systems resulted in the discovery of the first itinerant antiferromagnet composed of non-magnetic elements TiAu. The spin density wave antiferromagnetic ordering separates this compound from the previously reported ferromagnetic ones. Furthermore, perturbation of TiAu lattice with doping resulted in an antiferromagnetic quantum critical point, which can provide insights on the validity of the self-consistent renormalization theory of spin fluctuations in itinerant magnets.