Coherent Raman scattering (CRS) microscopy is a chemical imaging modality that provides contrast based on intrinsic biomolecular vibrations. To date, endeavors on instrumentation have advanced CRS into a powerful analytical tool for studies of cell functions and in situ clinical diagnosis. Nevertheless, the small cross-section of Raman scattering sets up a physical boundary for the design space of a CRS system, which trades off speed, signal fidelity and spectral bandwidth. The synergistic combination of instrumentation and computational approaches offers a way to break the trade-off. In this review, we first introduce coherent Raman scattering and recent instrumentation developments, then discuss current computational CRS imaging methods, including compressive micro-spectroscopy, computational volumetric imaging, as well as machine learning algorithms that improve system performance and decipher chemical information. We foresee a constant permeation of computational concepts and algorithms to push the capability boundary of CRS microscopy.