The fundamental constants of nature must fall within a range of values in order for the universe to develop structure and ultimately support life. This talk considers the current constraints on these quantities and assesses the degree of fine-tuning required for the universe to be viable. The first step is to determine what parameters are allowed to vary. In the realm of particle physics, we must specify the strengths of the fundamental forces and the particle masses. The relevant cosmological parameters include the density of the universe, the cosmological constant, the abundance of ordinary matter, the dark matter contribution, and the amplitude of primordial density fluctuations. These quantities are constrained by the requirements that the universe lives for a sufficiently long time, emerges from its early epochs with an acceptable chemical composition, and can successfully produce galaxies. On smaller scales, stars and planets must be able to form and function. The stars must have sufficiently long lifetimes and hot surface temperatures. The planets must be large enough to maintain atmospheres, small enough to remain non-degenerate, and contain enough particles to support a biosphere. We also consider specific fine-tuning issues in stars, including the triple alpha reaction that produces carbon, the case of unstable deuterium, and the possibility of stable diprotons. For all of these issues, the goal of this enterprise is to delineate the range of parameter space for which universes can remain habitable.