The authors describe recent experimental efforts to perform polarization-resolved optical spectroscopy of monolayer transition-metal dichalcogenide semiconductors in very large pulsed magnetic fields to 65 T. The experimental setup and technical challenges are discussed in detail, and temperature-dependent magnetoreflection spectra from atomically thin tungsten disulphide are presented. The data clearly reveal not only the valley Zeeman effect in these two-dimensional semiconductors but also the small quadratic excitondiamagnetic shift from which the very small exciton size can be directly inferred. Finally, the authors present model calculations that demonstrate how the measured diamagnetic shifts can be used to constrain estimates of the exciton binding energy in this new family of monolayer semiconductors.