We investigate the migration mechanism of the carbon vacancy (VC) in silicon carbide (SiC) using a combination of theoretical and experimental methodologies. The VC, commonly present even in state-of-the-art epitaxial SiC material, is known to be a carrier lifetime killer and therefore strongly detrimental to device performance. The desire for VC removal has prompted extensive investigations involving its stability and reactivity. Despite suggestions from theory that VC migrates exclusively on the C sublattice via vacancy-atom exchange, experimental support for such a picture is still unavailable. Moreover, the existence of two inequivalent locations for the vacancy in 4H-SiC [hexagonal, VC(h), and pseudocubic, VC(k)] and their consequences for VC migration have not been considered so far. The first part of the paper presents a theoretical study of VC migration in 3C- and 4H-SiC. We employ a combination of nudged elastic band (NEB) and dimer methods to identify the migration mechanisms, transition state geometries, and respective energy barriers for VC migration. In 3C-SiC, VC is found to migrate with an activation energy of EA=4.0 eV. In 4H-SiC, on the other hand, we anticipate that VC migration is both anisotropic and basal-plane selective. The consequence of these effects is a slower diffusivity along the axial direction, with a predicted activation energy of EA=4.2 eV, and a striking preference for basal migration within the h plane with a barrier of EA=3.7 eV, to the detriment of the k-basal plane. Both effects are rationalized in terms of coordination and bond angle changes near the transition state. In the second part, we provide experimental data that corroborates the above theoretical picture. Anisotropic migration of VC in 4H-SiC is demonstrated by deep level transient spectroscopy (DLTS) depth profiling of the Z1/2 electron trap in annealed samples that were subject to ion implantation. Activation energies of EA=(4.4±0.3) eV and EA=(3.6±0.3) eV were found for VC migration along the c and a directions, respectively, in excellent agreement with the analogous theoretical values. The corresponding prefactors of D0=0.54cm2/s and 0.017cm2/s are in line with a simple jump process, as expected for a primary vacancy point defect.