Quantum field theory is the theoretical framework of particle physics. Without it, we never could have worked out what an atom is made of, understood the forces that govern its content, or predicted the Higgs boson.
But when it was first being established in the first half of the 20th century, it came across an apparently fatal flaw. It was plagued with infinities. And infinities don’t belong in physics. Following the rules of quantum field theory, you could end up predicting an electron having an infinite electric charge. Gasp. Its resolution lead to a revolutionised way of thinking that now underpins all of particle physics.