A century after the discovery of quantum mechanics, the meaning of quantum
mechanics still remains elusive. This is largely due to the puzzling nature of
the wave function, the central object in quantum mechanics. If we are realists
about quantum mechanics, how should we understand the wave function? What does
it represent? What is its physical meaning? Answering these questions would
improve our understanding of what it means to be a realist about quantum
mechanics. In this survey article, I review and compare several realist
interpretations of the wave function. They fall into three categories:
ontological interpretations, nomological interpretations, and the \emph{sui
generis} interpretation. For simplicity, I will focus on non-relativistic
quantum mechanics.Comment: Penultimate version for Philosophy Compas