Carbon-enhanced metal-poor (CEMP) stars are known to have properties that reflect the nucleosynthesis of the first low- and intermediate- mass stars, because most have been polluted by a now-extinct AGB star. By considering abundances in the various CEMP subclasses separately, we try to derive parameters (such as metallicity, mass, temperature, and neutron source) characterising AGB nucleosynthesis from the specific signatures imprinted on the abundances, and separate them from the impact of thermohaline mixing, first dredge-up, and dilution associated with the mass transfer from the companion. To place CEMP stars in a broader context, we collect abundances for about 180 stars of various metallicities (from solar to [Fe/H]=-4), luminosity classes (dwarfs and giants), and abundance patterns (e.g. C-rich and poor, Ba-rich and poor), from both our own sample and the literature.