Spectroscopic experiments on molecules embedded in free clusters of liquid helium reveal a number of unusual features deriving from the unique quantum behavior of this nanoscale matrix environment. The apparent free rotation of small molecules in bosonic He-4 clusters is one of the experimentally most well documented of these features. In this Focus article, we set this phenomenon in the context of experimental and theoretical advances in this field over the last ten years, and describe the microscopic insight which it has provided into the nature and dynamic consequences of quantum solvation in a superfluid. We provide a comprehensive theoretical analysis which is based on a unification of conclusions drawn from diffusion and path integral Monte Carlo calculations. These microscopic quantum calculations elucidate the origin of the empirical free rotor spectrum, and its relation to the boson character and superfluid nature of the quantum nanosolvent. The free rotor behavior of the molecular rotation is preserved because of inefficient angular momentum coupling between the dopant and its quantum liquid surroundings. This is consistent with the superfluid character of the droplet, and has significant implications for the hydrodynamic response of the local quantum fluid environment of the embedded molecule. The molecule-helium interaction appears to induce a local nonsuperfluid density component in the first quantum solvation shell. This can adiabatically follow the molecular rotation, resulting in a reduction of the rotational constant. The dynamic nature of this adiabatically following density, its relation to the magnitude of the gas-phase molecular rotational constant and to the anisotropy of the interaction potential, are characterized with several examples. The role of the local superfluid density is analyzed within a continuum hydrodynamic model which is subject to microscopic quantum constraints. The result is a consistent theoretical framework which unites a zero temperature description based on analysis of cluster rotational energy levels, with a quantum two-fluid description based on finite temperature analysis of local quantum solvation structure in the superfluid.