We discuss semiclassical approximations of the spectrum of the periodically kicked top, both by diagonalizing the semiclassically approximated Floquet matrix F and by employing periodic-orbit theory. In the regular case when F accounts only for a linear rotation periodic-orbit theory yields the exact spectrum. In the chaotic case the first method yields the quasienergies with an accuracy of better than 3% of the mean spacing. By working in the representation where the torsional part of the Floquet matrix is diagonal our semiclassical work is mostly an application of the asymptotics of the rotation matrix, i.\,e.~of Wigner's so-calledd -functions.