Midwavelength infrared (MWIR) hyperspectral imaging using imaging Fourier transform spectrometers (IFTSs) is a potent way to quantify gas and particle-phase pollutants from combustion processes based on thermal emission from the plume. IFTSs generate data cubes containing thousands of images, each at a unique wavelength. Species may then be fingerprinted from their spectral signature, and column densities may be mapped over a scene by inverting a spectroscopic model derived from the radiative transfer equation. Column density maps are then combined with a projected velocity field obtained from a sequence of images to obtain mass fluxes. While this passive technique shows promise and presents significant advantages over competing active approaches, there remain challenges associated with inverting the spectroscopic model, which is ill-posed, as well as spectral artifacts induced by turbulent fluctuations in the gas. This paper summarizes the state-of-the-art of this approach, and presents three case studies: a steamassisted flare, an enclosed combustor, and a smokestack at a refinery.