Magnetism is a fascinating phenomenon with roots in the ancient world. Although its precise understanding calls for relativistic quantum mechanics and field theory, it is integral to everyday technologies. In magnetic insulators, electrons are closely bound to a crystal lattice and carry strongly interacting magnetic dipoles; as a result, phases of matter with no classical analogs are possible. Such quantum magnetic phases are of great fundamental interest as a testbed of our understanding of many-particle quantum mechanics. In the first part of this lecture, I will discuss some of the central ideas in quantum magnetism, from the Heisenberg model to the more recent concepts introduced by Kitaev and others. Then, I will explain our research program to search for these simple models in bulk materials and understand their properties using neutron spectroscopy.