The fundamental theory of the strong interactions of quarks and gluons is quantum chromodynamics (QCD). I will start this seminar with an introduction to the basic equations of QCD by way of comparison with quantum electrodynamics, and explain why calculations in QCD at energy scales relevant to the physics of hadrons must be done nonperturbatively. I will then introduce the lattice formulation and show the steps involved in obtaining first-principles predictions from nonperturbative QCD using simulations on supercomputers. Finally, I will present a small selection of results from lattice QCD, beginning with the phenomenology of the strong interactions and then proceeding to searches for physics beyond the Standard Model, where QCD plays the role of a "background" that must be calculated precisely to find small signals of other interactions.