Molecular rotors are a group of fluorescent molecules that form twisted intramolecular charge transfer (TICT) states upon photoexcitation. When intramolecular twisting occurs, the molecular rotor returns to the ground state either by emission of a red-shifted emission band or by nonradiative relaxation. The emission properties are strongly solvent-dependent, and the solvent viscosity is the primary determinant of the fluorescent quantum yield from the planar (non-twisted) conformation. This viscosity-sensitive behavior gives rise to applications in, for example, fluid mechanics, polymer chemistry, cell physiology, and the food sciences. However, the relationship between bulk viscosity and the molecular-scale interaction of a molecular rotor with its environment are not fully understood. This review presents the pertinent theories of the rotor-solvent interaction on the molecular level and how this interaction leads to the viscosity-sensitive behavior. Furthermore, current applications of molecular rotors as microviscosity sensors are reviewed, and engineering aspects are presented on how measurement accuracy and precision can be improved.