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Increasingly, uncertainties in predictions from galaxy formation simulations (at sub-Milky Way masses) are dominated by uncertainties in stellar evolution inputs. In this paper, we present the full set of updates from the FIRE-2 version of the Feedback In Realistic Environments (FIRE) project code, to the next version, FIRE-3. While the transition from FIRE-1 to FIRE-2 focused on improving numerical methods, here we update the stellar evolution tracks used to determine stellar feedback inputs, e.g. stellar mass-loss (O/B and AGB), spectra (luminosities and ionization rates), and supernova rates (core-collapse and Ia), as well as detailed mass-dependent yields. We also update the low-temperature cooling and chemistry, to enable improved accuracy at $T \lesssim 10^{4}\,$K and densities $n\gg 1\,{\rm cm^{-3}}$, and the meta-galactic ionizing background. All of these synthesize newer empirical constraints on these quantities and updated stellar evolution and yield models from a number of groups, addressing different aspects of stellar evolution. To make the updated models as accessible as possible, we provide fitting functions for all of the relevant updated tracks, yields, etc, in a form specifically designed so they can be directly 'plugged in' to existing galaxy formation simulations. We also summarize the default FIRE-3 implementations of 'optional' physics, including spectrally-resolved cosmic rays and supermassive black hole growth and feedback.