Particles with strong interactions have universal low-energy properties independent of the details of the short-distance dynamics. Such systems occur in many areas of physics, including ultracold atoms, hadrons, and nuclei. In the unitary limit of infinite scattering length, the interactions do not provide a length scale. Thus the effective field theory describing such a system is invariant under scale and conformal transformations. I will discuss recent applications of this theory and future challenges with an emphasis on nuclear and particle physics.