In this talk, I will give a brief introduction to Heavy Quarkonium physics, the general procedures in the higher-order computations (including the basic tools used in the automatic calculations), and a short report on our recent works about two loop computations in Quarkonium process, involving the 1st heavy Quarkonium production process: \gamma \gamma^{\ast} \rightarrow \eta_c and 1st inclusive decay process: \eta_c \rightarrow Light Hadrons at next-to-next-to-leading-order (NNLO).