With the discovery of the Higgs boson the Standard Model is complete and high energy physics has entered a new era of exploration. We have good reason to be optimistic as several empirical mysteries cry out for physics beyond the Standard Model. Unfortunately, the energy scale associated with this new physics is unknown, and therefore we must strive to search for new phenomena using all means at our disposal. With this overarching motivation, a vigorous and diverse experimental program has emerged to advance explorations at the intensity frontier and search for new light particles with extremely weak couplings to ordinary matter. Such new states may play a role in addressing the dark matter and neutrino mass problems, among others. In this talk, I will review the physics motivation for this program and highlight some of the novel theoretical and experimental approaches that take aim at exotic light new physics.