Deep learning (DL) has revolutionized bioimage analysis, enabling unprecedented insights into cellular dynamics. This review provides an overview of state-of-the-art DL approaches for quantifying cellular dynamics from 2D microscopy images, considering the three fundamental steps in dynamics analysis: identifying objects in space through segmentation, connecting them through time via tracking, and extracting meaningful measurements from their resulting trajectories. We highlight how recent methodological innovations in DL are complementing more classical, long-established algorithms, and discuss emerging trends as well as the importance of ensuring that DL-powered cellular dynamics analysis remains scientifically sound and accessible. By discussing methodological advances and pointing to available practical tools, this review aims to bridge the gap between computational expertise and biological applications, providing guidance to help navigate this rapidly evolving field and identify approaches that are relevant to specific research questions.