The structure and kinematics of the LMC continue to be active areas of research. As outlined in this review, much progress has been made recently. Improved datasets have played a key role in this, most notably the advent of large stellar datasets of magnitudes in many bands, lightcurves, and line-of-sight kinematics, and also the availability of sensitive HI observations over large areas. As a result we now have a fairly good understanding of the LMC morphology and kinematics. The proper motion of the LMC is reasonably well measured and the global properties of the LMC orbit around the Milky Way are understood. The angles that determine how we view the LMC are now known much more accurately than before and this has led to the realization that the LMC is quite elliptical in its disk plane. We are starting to delineate the vertical structure of the LMC and are finding complexities that were not previously expected.
Despite the excellent progress, many questions on LMC structure still remain open. Why is the bar offset from the center of the outer isophotes of the LMC? Why is the dynamical center of the HI offset from the center of the bar, from the center of the outer isophotes, and from the dynamical center of the carbon stars? Why do studies of the inner and outer regions of the LMC yield differences in line-of-nodes position angle of up to 30°? Does the LMC have a pressure supported halo? Are there populations of stars at large distances from the LMC plane? What is the origin and dynamical nature of the non-planar structures detected in the inner regions of the LMC? Do different tracers outline the same non-planar structures?
It might be necessary to answer all of these open questions before we can convince ourselves that the optical depth for LMC self-lensing has been correctly estimated. This seems to be the most critical step in establishing whether or not the Milky Way halo contains hitherto unknown compact lensing objects (MACHOs). The open questions about LMC structure are important also in their own right. The tidal interaction between the Magellanic Clouds and the Milky Way provides one of our best laboratories for studying the processes of tidal disruption and hierarchical merging by which all galaxies are believed to grow. A better understanding of LMC structure may also provide new insight into the origin of the Magellanic Stream, which continues to be debated. And with improved proper motion measurements of the Magellanic Clouds, the Stream may become a unique tool to constrain the shape and radial density distribution of the Milky Way halo at radii inaccessible using other tracers.