While tropical cyclones (TCs) are axisymmetric vortices to the first order, they often exhibit noteworthy structural asymmetries. These often result from environmental vertical wind shear, which tilts the vortex and induces a wavenumber 1 pattern in the circulation and precipitation fields. Reanalyses and climate models have improved in representing the TC structure and climatology, but their relatively coarse resolution and dependence on parameterized physics cast doubt on their ability to capture the asymmetric TC structure. We perform the most comprehensive process-oriented assessment of TC asymmetry to date in reanalyses. Specifically, we analyze the composite shear-relative TC structure in ERA5 and Climate Forecast System Reanalysis (CFSR), which vary in their resolutions, physical parameterization suites, and data assimilation techniques. These structures are compared with aircraft reconnaissance radar observations. In agreement with the observations, the strongest tangential winds are usually found left-of-shear, while inner core rainfall, ascent, vortex tilt, and low-level inflow are favored directly downshear or in the downshear-left quadrant. Outer rainband convection generally peaks in the downshear-right quadrant. Thermodynamic asymmetries are also apparent, with anomalous low-level moisture right-of-shear, midlevel warmth in the upshear-right quadrant (uptilt), and cloud properties suggestive of a realistic precipitation life cycle from growth to fallout. We also decompose rainfall contributions from the convective parameterization and large-scale cloud schemes and highlight the roles of vorticity advection, buoyancy advection, and diabatic processes in driving asymmetric vertical motions in the inner core and outer rainband regions. Our results suggest that process-level studies of TC asymmetry and TC–wind shear interaction under future warming are viable using climate models. Significance Statement Asymmetries are common in tropical cyclones (TCs), influencing their intensity, track, and hazards. Vertical wind shear often plays a leading-order role in causing these asymmetries. It is uncertain how well asymmetric structures and processes are captured in reanalyses and global climate models (GCMs) with grid spacings of 0.25° and coarser. In this study, we first evaluate TC asymmetry in reanalyses, which have the benefit of being forced by observations. This helps to assess whether the resolutions associated with GCMs sufficiently capture asymmetric structures and processes and motivates upcoming work with free-running GCMs to study how TC asymmetry may change in a warming climate.