Magnetic resonance spectroscopic imaging (MRSI) offers a unique molecular window into the physiological and pathological processes in the human body. However, the applications of MRSI have been limited by a number of long-standing technical challenges due to high dimensionality and low signal-to-noise ratio (SNR). Recent technological developments integrating physics-based modeling and data-driven machine learning that exploit unique physical and mathematical properties of MRSI signals have demonstrated impressive performance in addressing these challenges for rapid, high-resolution, quantitative MRSI. This paper provides a systematic review of these progresses in the context of MRSI physics and offers perspectives on promising future directions.