Droplet breakup of many Newtonian fluids is well described by current experiments, theory, and simulations. Breakup in complex fluids where interactions between mesoscopic structural features can affect the flows remains poorly understood and a burgeoning area of research. Here, we report on our investigations of droplet breakup in thermotropic liquid crystals. We investigate breakup in the smectic, nematic, and isotropic phases of 4-cyano 4-octylbiphenyl (8CB) and the nematic and isotropic phases of 4-cyano 4-pentylbiphenyl (5CB). The experiment consists of varying the ambient temperature to control liquid crystalline phase and imaging breakup using a fast video camera at up to 110000 frames/s. We expand on previous work that shows breakup in the smectic phase is symmetric, producing no satellite droplets, and is well described by a similarity solution for a shear-thinning power-law fluid. We show that in the nematic phase the breakup occurs in two stages. In the first stage, the breakup is symmetric and the power-law exponent for the minimum radius dependence on the time left to breakup is 1.2