Synopsis The methods of the existing literature on the subject are rearranged and supplemented in this general survey. With the symmetric rotator, the Hamiltonian H commutes with the component of angular momentum Pc along the symmetry axis of the rotator. The eigenfunctions of H prove to be identical with the simultaneous eigenfunctions Φ of the square of the angular momentum P2, the component of angular momentum P2 along an axis fixed in space, and Pc (Sec. 3). In the case of the asymmetric rotator, H does not commute with any component of angular momentum in a direction fixed in the rotator. The eigenfunctions of H may now be written as linear combinations of functions Φ (Sec. 4). As a new method, we use instead of the Φ closely connected functions Φ5 adapted to the four-group symmetry of the asymmetric rotator (Sec. 5). The secular equation then splits immediately into four factors related to the four possible symmetry species of the eigenfunctions (Sec. 6). The confusion resulting from the various choices of the phases of matrix elements and wave functions is cleared (Sec. 7). Some algebraic properties important for calculating the energy values are treated. The position of the levels is illustrated by a figure, which has been drawn with the aid of tables supplied by King, Hainer and Cross1). The symmetry classification can be found from the sequential order of the eigenvalues, a result particularly important for practical application (Sec. 8). In conclusion, the selection rules for dipole radiation are given (Sec. 9).