Small molecules constructed from familiar chemical components, but with an unconventional (reduced symmetry) molecular shape, hold promise for developing nematic liquid crystals with macroscopic biaxiality or even polarity. These properties, realized over practical temperature ranges using thermotropic compounds, could open new avenues in technologies including optical displays, mechanical sensors, and low-cost personal power generation. I will report on recent studies of short-range order – a guidance, if not a direct precursor, to rational development of biaxial/polar nematics – in three types of reduced symmetry thermotropic materials: bent-core (V-shaped) liquid crystal compounds and rod-like molecules containing either lateral branches (Y-shaped) or bridges (H-shaped). These studies, performed with synchrotron small-angle X-ray scattering, indicate a common feature of staggered layer (smectic-C-like) short-range molecular order, which is observed in the full nematic range and even in the absence of any lower temperature smectic phase. Quantitative modeling of the SAXS patterns demonstrates that the order is best described by finite-sized nanodomains rather than by the average effect of order parameter fluctuations. The analysis also reveals interesting correlations between molecular structure and the anisotropy of the nanodomains and their temperature dependence. Additionally I will review efforts by collaborators at KSU to visualize directly the domain structure by cryo-TEM techniques. Finally, I will summarize some of the positive (and negative) aspects of the macroscopic properties of the materials evaluated so far.