The abundance patterns of the most metal-poor stars in the Galactic halo and small dwarf galaxies provide us with a wealth of information about the early Universe. In particular, these old survivors allow us to study the nature of the first stars and supernovae, the relevant nucleosynthesis processes responsible for the formation and evolution of the elements, early star- and galaxy formation processes, as well as the assembly process of the stellar halo from dwarf galaxies a long time ago. This review presents the current state of the field of "stellar archaeology" -- the diverse use of metal-poor stars to explore the high-redshift Universe and its constituents. In particular, the conditions for early star formation are discussed, how these ultimately led to a chemical evolution, and what the role of the most iron-poor stars is for learning about Population III supernovae yields. Rapid neutron-capture signatures found in metal-poor stars can be used to obtain stellar ages, but also to constrain this complex nucleosynthesis process with observational measurements. Moreover, chemical abundances of extremely metal-poor stars in different types of dwarf galaxies can be used to infer details on the formation scenario of the halo and the role of dwarf galaxies as Galactic building blocks. I conclude with an outlook as to where this field may be heading within the next decade. A table of ~1000 metal-poor stars and their abundances as collected from the literature is provided in electronic format.