Cosmological observations give us some of the clearest views of the history of the universe and the laws that shaped it. Yet, despite the incredible progress, our view is still quite limited. The next generation of observations will break new ground in our sensitivity to earlier times in our thermal history. In this colloquium, I will review the status of our understanding of the early universe from current data. I will then highlight the measurement of cosmic neutrino background and the search for additional light relics of the hot big bang using current and future cosmological surveys. I will explain why these measurements are robust and how they are important as a probe of fundamental physics. I will discuss several targets that can be achieved from the CMB with the Simons Observatory and CMB Stage 4, and the potential for improvements from future galaxy surveys.