Solving QFT is key to a more profound understanding of present and next generation of theories of Nature. In fact, both the large number-of-flavour 1/Nf and charge 1/Q expansion have been useful tools to go beyond Feynman diagrammatic computations. In this talk, I will discuss not only the theoretical perspectives of these two methods but, in particular, also their important applications in particle physics phenomenology. I will show that by using the large number-of-flavour 1/Nf summation techniques, the Standard Model can achieve an interacting ultraviolet fixed point to be asymptotically safe, addressing the famous UV Landau Pole problem. The large charge 1/Q approach may have the potential to address the multi-Higgs production problem. I will show that by implementing the large charge 1/Q approach, we can determine the scaling dimensions of a class of fixed charge operators to the next-to-leading-order in the charge expansion but to all orders in their couplings.