While the Standard Model (SM) of particle physics provides the current best description of the sub-atomic nature of the known Universe, there are many observations with which the SM cannot be reconciled. Direct searches for beyond the SM (BSM) physics have thus far not discovered anything, and the possibility remains that any BSM particles are beyond direct reach of the Large Hadron Collider. Fortunately, precision measurements of the SM are also powerful indirect tests of BSM physics. I will discuss precision measurements of rare electroweak processes performed at the ATLAS experiment, including measurements of vector boson scattering and the production of multiple vector bosons. These measurements help us both to better understand the SM and to perform generic searches for new phenomena through effective field theory decompositions.