The Core Imaging Library (CIL) is an open-source Python framework for tomographic imaging with particular emphasis on reconstruction of challenging datasets. Conventional filtered backprojection reconstruction tends to be insufficient for highly noisy, incomplete, non-standard or multichannel data arising for example in dynamic, spectral and in situ tomography. CIL provides an extensive modular optimisation framework for prototyping reconstruction methods including sparsity and total variation regularisation, as well as tools for loading, preprocessing and visualising tomographic data.