The strong force is governed by the elegant mathematical framework of quantum chromodynamics (QCD). The building blocks of QCD are quarks and gluons, and the interactions of these constituents lead to a rich variety of observed phenomena, from the basic properties of nuclei to the production of heavy elements in stars. A particularly intriguing aspect of QCD is the nature of resonances, short lived states that decay via the strong force. Many exotic resonances have been discovered over the last decade, with properties that are not easily described in simplified models of QCD. In addition, such excitations can dramatically affect the properties of electroweak decays so that a detailed understanding is crucial for expanding searchers of new physics beyond the Standard Model. In this talk I will discuss progress in theoretically controlling such effects in a rigorous and quantitative way by combining field theoretic ideas with large scale computer simulations in the framework of lattice QCD.