Nuclear structure physics has presented a fruitful testing ground for quantum many-body theory since its beginnings half a century ago. On the one hand, the observed phenomena have given rise to models that have been invaluable to interpret the underlying physics. On the other hand, the quest to make a predictive theory has given strong impetus to developing computational tools to solve the many-particle Schroedinger equation. I will review some of these theoretical highlights in nuclear structure, ranging from the modeling and computation of few-body systems to the many-particle finite systems represented by our heavy nuclei. Among the models I discuss are the unitary-limit fermionic Hamiltonian, the Nilsson model of nuclear deformations, and the Richardson-Gaudin model of pairing. Computational strategies that have been very successful in different contexts are the Monte-Carlo methods, the multi-configuration shell model, and the extensions of mean-field theory to restore broken symmetries.