A surprisingly large fraction of metal-poor stars are found to be
carbon-rich. In addition, many of these display enhancements of neutron
capture elements which give clues to their origin. I will discuss what
we think we know about these so-called carbon-enhanced metal-poor (CEMP)
stars, with a focus on those that display barium enrichments. These
CEMP stars are thought to be formed in binary star systems that formerly
contained an asymptotic giant branch (AGB) star, which polluted its
companion through mass transfer. I will review our picture of AGB
nucleosynthesis at low metallicity, how we think mass transfer happens
and what happens to material once it is accreted by the secondary. This
will highlight the problems we have when we try to confront observed
CEMP star abundances with predictions from increasingly detailed stellar
models.