Recent work has demonstrated the existence of 3D Weyl semimetals, unique topologically protected states of matter with linearly dispersing excitations in their bulk. While most of the study have focused on nonmagnetic, inversion symmetry breaking systems, a growing attention has been paid to another type of Weyl semimetals induced by collective magnetic order, as they may exhibit various types of novel phenomena that would be useful for spintronics and energy harvesting applications. We shall design, synthesize, and characterize materials that harbor this new state of matter – magnetic Weyl fermions borne of correlations. In related work we will also investigate a new class of materials with quadratic band touchings – the Luttinger semimetal state. Such systems are predicted to be generically strongly interacting and show non-Fermi liquid correlations.