Elemental abundance patterns in very metal-poor halo field stars and globular cluster stars play a crucial role both in guiding theoretical models of nucleosynthesis and in providing constraints upon the early star formation and concomitant nucleosynthesis history of our Galaxy. The abundance patterns characterizing the oldest and most metal deficient stars ([Fe/H] ≤ −3) are entirely consistent with their being products of metal-poor massive stars of lifetimes τ ≤ 108 years. This includes both the elevated abundances of the alpha-elements (O, Mg, Si, S, Ca, and Ti) relative to iron-peak elements and the dominance of r-process elements over s-process elements. The nucleosynthetic contributions of lower mass AGB stars of longer lifetimes (τ ≈ 109 years) begin to appear at metallicities [Fe/H] ≈ −2.5, while clear evidence for iron-peak nuclei produced in supernovae Ia (τ ≥ 1-2x109 years?) does not appear until metallicities approaching [Fe/H] ~ −1. Similar trends are also suggested by abundances determined for gas clouds at high redshifts. We review the manner in which a knowledge of the abundances of the stellar and gas components of early populations, as a function of [Fe/H], time, and/or redshift, can be used to set constraints on their star formation and nucleosynthesis histories.