Spinels of the chemical formula AB2X4 are important systems in the study of frustrated magnetism. The A and B sites of spinels constitute diamond and pyrochlore lattices, respectively, whose special geometries can give rise to many exotic phenomena. In this thesis, we investigate the spin correlations in three types of frustrated spinels: the spin ice candidates CdEr2X4 (X = Se, S), the spiral spin-liquid candidate MnSc2S4, and the spin-Peierls system MgCr2O4.