I review our understanding of the structure and kinematics of the Large Magellanic Cloud (LMC), with a particular focus on recent results. This is an important topic, given the status of the LMC as a benchmark for studies of microlensing, tidal interactions, stellar populations, and the extragalactic distance scale. I address the observed morphology and kinematics of the LMC; the angles under which we view the LMC disk; its in-plane and vertical structure; the LMC self-lensing contribution to the total microlensing optical depth; the LMC orbit around the Milky Way; and the origin and interpretation of the Magellanic Stream. Our understanding of these topics is evolving rapidly, in particular due to the many large photometric and kinematic datasets that have become available in the last few years. It has now been established that: the LMC is considerably elongated in its disk plane; the LMC disk is thicker than previously believed; the LMC disk may have warps and twists; the LMC may have a pressure-supported halo; the inner regions of the LMC show unexpected complexities in their vertical structure; and precession and nutation of the LMC disk plane contribute measurably to the observed line-of sight velocity field. However, many open questions remain and more work is needed before we can expect to converge on a fully coherent structural, dynamical and evolutionary picture that explains all observed features of the LMC.