Mass is the fundamental parameter that governs the evolution of stars, brown dwarfs, and gas-giant planets. Thus, direct mass measurements are essential to test the evolutionary and atmospheric models that underpin studies of these objects. We present results from our program to test models using precise dynamical masses for visual binaries based on Keck laser guide star adaptive optics astrometric monitoring of a sample of over 30 ultracool (> M6) objects since 2005. In just the last 2 years, we have more than tripled the number of late-M, L, and T dwarf binaries with precise dynamical masses. For most field binaries, based on direct measurements of their luminosities and total masses, we find a "temperature problem" in that evolutionary model radii give effective temperatures that are inconsistent with those from model atmosphere fitting of observed spectra by 100-300 K. We also find a "luminosity problem" for the only binary with an independent age determination (from its solar-type primary via age activity rotation relations). Evolutionary models underpredict the luminosities of HD 130948BC by a factor of ≈2, implying that model-based substellar mass determinations (e.g., for directly imaged planets and cluster IMFs) may be systematically overestimating masses. Finally, we have employed the current sample of binary orbits to carry out a novel test of the earliest evolutionary stages, by using the distribution of orbital eccentricities to distinguish between competing models of brown dwarf formation.