Conformal field theories are non-trivial fixed points of quantum field theories. For the subclass of superconformal field theories (SCFTs) in dimension D>3, it is hoped that all of them can be constructed from parent 6D SCFTs. In this talk, I'm going to present our new tool kit to classify and study 5D N=1 SCFTs along this approach. Namely, each strongly coupled 5D N=1 SCFT is associated with a graph, which is called "combined fiber diagram". It explicitly contains the information about the flavor symmetry, BPS states, and transitions between different SCFTs. With this powerful tool, one can simply read off the enhanced flavor symmetry of a 5D N=1 gauge theory at its UV fixed point, which is very difficult to compute with other methods.