The proliferation of microscopy methods for live-cell imaging offers many new possibilities for users but can also be challenging to navigate. The prevailing challenge in live-cell fluorescence microscopy is capturing intra-cellular dynamics while preserving cell viability. Computational methods can help to address this challenge and are now shifting the boundaries of what is possible to capture in living systems. In this Review, we discuss these computational methods focusing on artificial intelligence-based approaches that can be layered on top of commonly used existing microscopies as well as hybrid methods that integrate computation and microscope hardware. We specifically discuss how computational approaches can improve the signal-to-noise ratio, spatial resolution, temporal resolution and multi-colour capacity of live-cell imaging.|The prevailing challenge in live-cell fluorescence microscopy is capturing intra-cellular dynamics while preserving cell viability. Alongside developments of microscopy hardware, computational methods - especially those based on machine learning - are powerful tools to improve the signal-to-noise ratio, spatial resolution, temporal resolution and multi-colour capacity of live-cell imaging.