The Standard Model of Particle Physics has been verified to unprecedented precision in the last few decades. However there are still phenomena in nature which cannot be explained, and as such new theories will be required. Since terrestrial experiments are limited in both the energy and precision that can be probed, new methods are required to search for signs of physics beyond the Standard Model. In this dissertation, I demonstrate how these theories can be probed by searching for remnants of their effects in the early Universe. In particular I focus on three possible extensions of the Standard Model: the addition of massive neutral particles as dark matter, the addition of charged massive particles, and the existence of higher dimensions. For each new model, I review the existing experimental bounds and the potential for discovering new physics in the next generation of experiments. For dark matter, I introduce six simple models which I have developed, and which involve a minimum amount of new physics, as well as reviewing one existing model of dark matter. For each model I calculate the latest constraints from astrophysics experiments, nuclear recoil experiments, and collider experiments. I also provide motivations for studying sub-GeV mass dark matter, and propose the possibility of searching for light WIMPs in the decay of B-mesons and other heavy particles. For charged massive relics, I introduce and review the recently proposed model of catalyzed Big Bang nucleosynthesis. In particular I review the production of Li6 by this mechanism, and calculate the abundance of Li7 after destruction of Be7 by charged relics. The result is that for certain natural relics CBBN is capable of removing tensions between the predicted and observed Li6 and Li7 abundances which are present in the standard model of BBN. For extra dimensions, I review the constraints on the ADD model from both astrophysics and collider experiments. I then calculate the constraints on this model from Big Bang nucleosynthesis in the early Universe. I also calculate the bounds on this model from Kaluza-Klein gravitons trapped in the galaxy which decay to electron-positron pairs, using the measured 511 keV gamma-ray flux. For each example of new physics, I find that remnants of the early Universe provide constraints on the models which are complimentary to the existing constraints from colliders and other terrestrial experiments.