Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning (ML) are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap encompasses key aspects of how ML is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of ML for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.