Kymographs are graphical representations of spatial position over time, which are often used in biology to visualise the motion of fluorescent particles, molecules, vesicles, or organelles moving along a predictable path. Although in kymographs tracks of individual particles are qualitatively easily distinguished, their automated quantitative analysis is much more challenging. Kymographs often exhibit low signal-to-noise-ratios (SNRs), and available tools that automate their analysis usually require manual supervision. Here we developed KymoButler, a Deep Learning-based software to automatically track dynamic processes in kymographs. We demonstrate that KymoButler performs as well as expert manual data analysis on kymographs with complex particle trajectories from a variety of different biological systems. The software was packaged in a web-based 'one-click' application for use by the wider scientific community (http://kymobutler.deepmirror.ai). Our approach significantly speeds up data analysis, avoids unconscious bias, and represents another step towards the widespread adaptation of Machine Learning techniques in biological data analysis.