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Micrographs of materials contain microstructural information that is quantifiable in principle, but difficult to extract in practice. We present Automatic QUantitative Analysis of Microscopy Images (AQUAMI): a Python package which can automatically analyze micrographs and extract quantitative information to characterize microstructure features. This software package utilizes digital image analysis methods to perform many thousands of measurements on an image and reports information such as the mean feature dimensions, size distribution, and phase area fraction. Results are repeatable and can be directly compared between research groups. The results are robust against large changes in magnification, focus, illumination, and noise. We describe the working principle of the software and demonstrate it on micrographs of nanoporous and nanocomposite metals.