We review the major advances in understanding the morphologies and kinematics of supernova remnants (SNRs). Simulations of SN explosions have improved dramatically over the last few years, and SNRs can be used to test models through comparison of predictions with SNRs’ observed large-scale compositional and morphological properties as well as the three-dimensional kinematics of ejecta material. In particular, Cassiopeia A—the youngest known core-collapse SNR in the Milky Way—offers an up-close view of the complexity of these explosive events that cannot be resolved in distant, extragalactic sources. We summarize the progress in tying SNRs to their progenitors’ explosions through imaging and spectroscopic observations, and we discuss exciting future prospects for SNR studies, such as X-ray microcalorimeters.