We give a full account of our extensive measurements of vortex mutual friction in rotating superfluid 3He, in both the A- and B-phases. The B-phase results are in qualitative agreement with a theory based on the concept of "spectral flow"; the agreement becomes quantitative if an effective energy gap of 0.63Δ is used, but the justification for such a substitution is not clear. The vortex core transition, at first not seen because of metastability and hysteresis, has now been observed. Detailed investigation suggests that the high temperature vortex state is a temperature dependent mixture of at least two vortex types. The A-phase mutual friction is found to be well described by two hydrodynamic coefficients, the orbital viscosity and the orbital inertia. The latter corresponds to an orbital angular momentum per Cooper pair of (0.0015 ± 0.0017) ℏ, consistent with the prediction of the spectral flow theory. We find that the most uniform l texture is obtained by cooling through Tc while rotating, and then stopping rotation. Detailed investigation of textural memory effects shows that the uniform l-up and l-down textures are associated with opposite directions of rotation. We discuss the various types of texture that may be formed in our experiments. Finally, we compare our mutual friction results with those found in 4HeII.