This work highlights the importance of in situ experiments for an improved understanding of graphene growth on copper via metal-catalyzed chemical vapor deposition (CVD). Graphene growth inside the chamber of a modified environmental scanning electron microscope under relevant low-pressure CVD conditions allows visualizing structural dynamics of the active catalyst simultaneously with graphene nucleation and growth in an unparalleled way. It enables the observation of a complete CVD process from substrate annealing through graphene nucleation and growth and, finally, substrate cooling in real time and nanometer-scale resolution without the need of sample transfer. A strong dependence of surface dynamics such as sublimation and surface premelting on grain orientation is demonstrated, and the influence of substrate dynamics on graphene nucleation and growth is presented. Insights on the growth mechanism are provided by a simultaneous observation of the growth front propagation and nucleation rate. Furthermore, the role of trace amounts of oxygen during growth is discussed and related to graphene-induced surface reconstructions during cooling. Above all, this work demonstrates the potential of the method for in situ studies of surface dynamics on active metal catalysts.