Infrared (IR) spectromicroscopy, or chemical imaging, is an evolving technique that is poised to make significant contributions in the fields of biology and medicine. Recent developments in sources, detectors, measurement techniques and speciman holders have now made diffraction-limited Fourier transform infrared (FTIR) imaging of cellular chemistry in living cells a reality. The availability of bright, broadband IR sources and large area, pixelated detectors facilitate live cell imaging, which requires rapid measurements using non-destructive probes. In this work, we review advances in the field of FTIR spectromicroscopy that have contributed to live-cell two and three-dimensional IR imaging, and discuss several key examples that highlight the utility of this technique for studying the structure and chemistry of living cells.