The early chemical evolution of the Galaxy and the Universe is vital to our understanding of a host of astrophysical phenomena. Since the most metal-poor Galactic stars (with metallicities down to [Fe/H] ∼ −5.5) are relics from the highredshift Universe, they probe the chemical and dynamical conditions of the Milky Way and the origin and evolution of the elements through nucleosynthesis. They also provide constraints on the nature of the first stars, their associated supernovae and initial mass function, and early star and galaxy formation. The Milky Way's dwarf satellites contain a large fraction (∼ 30%) of the known most metal-poor stars that have chemical abundances that closely resemble those of equivalent halo stars. This suggests that chemical evolution may be universal, at least at early times, and that it is driven by massive, energetic SNe. Some of these surviving, ultra-faint systems may show the signature of just one such Pop III star; they may even be surviving first galaxies. Early analogs of the surviving dwarfs may thus have played an important role in the assembly of the old Galactic halo whose formation can now be studied with stellar chemistry. Following the cosmic evolution of small halos in simulations of structure formation enables tracing the cosmological origin of the most metalpoor stars in the halo and dwarf galaxies. Together with future observations and additional modeling, many of these issues, including the reionization history of the Milky Way, may be constrained this way. The chapter concludes with an outlook about upcoming observational challenges and ways forward is to use metal-poor stars to constrain theoretical studies.