Abstract: Pulsar timing array experiments aim to detect nHz-frequency gravitational waves using high-precision timing of millisecond pulsars. Of particular interest is a stochastic gravitational wave background (SGWB), which is expected to arise predominantly from a population of inspiraling supermassive black hole binaries, but there may also be contributions from exotic cosmological sources, such as inflation, first-order phase transitions, and topological defects. On behalf of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration, I will present the search for a SGWB using the latest 15-year NANOGrav data. I will show the results of our analyses for various early universe physics scenarios, as well as searches for signatures of dark matter models that impart deterministic signals in the timing data, and discuss future prospects.