Over more than 30 years in vivo MR spectroscopic imaging (MRSI) has undergone an enormous evolution from theoretical concepts in the early 1980s to the robust imaging technique that it is today. The development of both fast and efficient sampling and reconstruction techniques has played a fundamental role in this process. Stateof-the-art MRSI has grown from a slow purely phase-encoded acquisition technique to a method that today combines the benefits of different acceleration techniques.These include shortening of repetition times, spatial-spectral encoding, undersampling of k-space and time domain, and use of spatial-spectral prior knowledge in the reconstruction. In this way in vivo MRSI has considerably advanced in terms of spatial coverage, spatial resolution, acquisition speed, artifact suppression, number of detectable metabolites and quantification precision. Acceleration not only Abbreviations: B0, static magnetic field strength; B1 + , transmit RF field; CAIPIRINHA, controlled aliasing in parallel imaging results in higher acceleration; CRT, concentric ring trajectory; CS, compressed sensing; CSDE, chemical shift displacement error; EPI, echo planar imaging; EPSI, echo-planar spectroscopic imaging; FID, free induction decay; FIDLOVS, FID acquisition localized by outer volume suppression; GRAPPA, generalized autocalibrating partially parallel acquisition; GSLIM, generalized series approach to MR spectroscopic imaging; IDEAL, iterative decomposition of water and fat with echo asymmetry and least-