Conventional magnetic resonance spectroscopic imaging (MRSI) is a Fourier transform-based imaging technique. During data acquisition, Fourier encodings or (k , t )-space data are acquired. Decoding (or image reconstruction) is often accomplished using the truncated Fourier series. To overcome the well-known limited-data problem with Fourier transform MRSI, several constrained MRSI methods have been developed to exploit prior knowledge to improve the coding (data acquisition) and decoding (image reconstruction) process. This article reviews two of these constrained MRSI methods: SLIM (Spectral Localization by IMaging) and SPICE (SPectroscopic Imaging by exploiting spatiospectral CorrElation). SLIM is a classical method designed to use explicit boundary information obtained from anatomical imaging to improve spectral localization; SPICE is a modern method that exploits the subspace (or low-rank) structure of spatiospectral functions for efficient spatiospectral encoding and high-quality image reconstruction from sparsely sampled data.