We discuss the principles underlying higher spin glueball calculations on the lattice. Comments on the use of variance reduction techniques will also be made. We present results on the glueball spectrum of the SU(2) gauge theory in 2+1 dimensions for spins ranging from 0 to 6, as well as preliminary results for SU(3) in 3+1 dimensions. Simple glueball models and the hypothetical relation of the even-spin spectrum to the 'pomeron' are discussed in both cases.