All frontiers of high energy physics aim to discover and understand the constituents of matter and the interactions at the highest energies, at the shortest distance, and at the earliest times in the Universe. The Standard Model of particle physics fails to explain all observed phenomena and new interactions and yet unseen particles must exist. They may manifest themselves either directly, as new particles, or by causing the Standard Model reactions to differ from often very precise predictions. The Intensity Frontier explores these fundamental questions by searching for new physics in processes extremely rare or those forbidden in the Standard Model. This requires the greatest possible beam intensities, as well as massive, ultra-sensitive detectors. Many of these experiments are sensitive to new physics at higher mass scales, or weaker interaction strengths, than those directly accessible at the LHC, thus providing opportunities for paradigm-changing new discoveries complementary to Energy and Cosmic Frontier experiments. In any new physics scenario, Intensity Frontier experiments with sensitivities to very high mass scales will be a primary tool for exploration. In this colloquium, I will describe the science opportunities at the Intensity Frontier.