A comprehensive theoretical and experimental study of the C-13 and Se-77 nuclear magnetic shieldings and their rovibrational corrections in carbon diselenide (CSe2) has been undertaken, The C-13 and Se-77 shielding tensors as well as all their first and second derivatives with respect to the internal displacement coordinates of the molecule have been calculated by several first principles gauge-including atomic orbital (GIAO) methods, Hartree-Fock (HF), multiconfiguration Hartree-Fock (MCHF), and density-functional (DFT) theories have been compared, the latter both in the local density approximation (LDA) and by using two gradient corrected exchange-correlation functionals. The shielding derivatives calculated with MCHF and DFT an very much smaller in magnitude than the derivatives obtained by using h-LF, being in reasonable mutual agreement, By using the theoretical shielding derivatives and the cubic anharmonic force constants calculated within LDA, together with an experimental, harmonic force field, all the first and second order terms in the rovibrational contributions to the shielding constants and anisotropies have been worked out. The contributions to the shielding constants have been calculated for the various isotopomers of CSe2 at several temperatures, and the resulting theoretical temperature dependencies of the shielding constants, the isotope shifts and the temperature dependencies of the isotope shifts have been compared with the experimental results, There is excellent agreement between the theoretical and experimental results for Se-77. The agreement is not quite as good for the (anomalously small) shielding constant of C-13 and its rovibrational corrections, Contrary to what has been frequently assumed, none of the first and second order terms in the rovibrational contributions to the shielding constants can safely be neglected. In particular, the first order isotope effect due to change in the bond not directly attached to the observed nucleus is very important. Furthermore, the second order terms - including the bending and even cross terms - are essential in order to give a correct description of the isotope shifts.