We report a combined theoretical and microwave spectroscopy study of the internal dynamics of the benzene dimer, a benchmark system for dispersion forces. Although the extensive ab initio calculations and experimental work on the equilibrium geometry of this dimer have converged to a tilted T-shaped structure, the rich internal dynamics due to low barriers for internal rotation have remained largely unexplored. We present new microwave spectroscopy data for both the normal (C6H6)(2) and partially deuterated (C6D6)(C6H6) dimers. The splitting patterns obtained for both species are unraveled and understood using a reduced-dimensionality theoretical approach. The hindered sixfold rotation of the stem can explain the observed characteristic 1 : 2 : 1 tunneling splitting pattern, but only the concerted stem rotation and tilt tunneling motion, accompanied by overall rotation of the dimer, yield the correct magnitude of the splittings and their strong dependence on the dimer angular momentum J that is essential to explain the experimental data. Also the surprising observation that the splittings are reduced by 30% for the mixed (C6D6)(C)(C6H6)(S) dimer in which only the cap (C) in the T-shaped structure is deuterated, while the rotating stem (S) monomer is the same as in the homodimer, is understood using this approach. Stark shift measurements allowed us to determine the dipole moment of the benzene dimer, mu = 0.58 +/- 0.051 D. The assumption that this dipole moment is the vector sum of the dipole moments induced in the monomers by the electric field of the quadrupole on the other monomer yields a calculated value of mu = 0.63 D. Furthermore, the observed Stark behavior is typical for a symmetric top, another confirmation of our analysis.