Renormalization group (RG) is dubbed one of the most important advances in theoretical physics in the past 50 years. In this talk I will lay out the basic picture of RG and introduce its general framework - functional renormalization group equations (FRGE). I will discuss how this is used to study the flow equations of quantum gravity using common approximation techniques. Finally, I will talk about the significance of cut-off choices and what these imply for fixed point solutions.