Abstract: Heavy quarkonium system provides an ideal laboratory to investigate theoretical and phenomenological aspects of QCD deeply. We have recently computed the 2-loop quarkonium Hamiltonian. This is the first non-trivial calculation of the N^4 LO corrections to the quarkonium Hamiltonian, defined in the potential-NRQCD effective field theory. In the first part, we review phenomenological motivations to compute the Hamiltonian. In the latter part, we explain the procedure of this computation as well as theoretically interesting points, and then we present the new results and some phenomenological impacts.