Epitaxial growth of graphene on Ru(0001) was investigated by photoemission electron microscopy (PEEM) and scanning tunneling microscopy (STM). By connecting the mesoscopic length scale of PEEM and the microscopic length scale of STM, we show that graphene overlayers with sizes ranging from nanometers to sub-millimeters have been prepared on Ru(0001) in a well-controllable fashion. From the systematic investigation of different methods to grow graphene on Ru(0001), the dominant factors in the graphene growth process have been revealed, which enables to grow graphene on transition metal surfaces in a controllable way. Additionally, the dynamic process of graphene etching by oxygen at temperatures between 600-1000 K was studied by in situ PEEM. The reaction kinetics results show that decrease in the graphene overlayers size is linearly dependent on the reaction time, indicating a reaction-controlled process. The catalytic effect of Ru substrate facilitates graphene oxidation, which shows relatively low activation energy of 27.2 kJ/mol.