The endoderm is a multipotent progenitor cell population in the embryo that gives rise to the liver, pancreas, and other cell types and provides paradigms for understanding cell-type specification. Studies of isolated embryo tissue cells and genetic approaches in vivo have defined fibroblast growth factor/mitogen-activated protein kinase (FGF/MAPK) and bone morphogenetic protein (BMP) signaling pathways that induce liver and pancreatic fates in the endoderm. In undifferentiated endoderm cells, the FoxA and GATA transcription factors are among the first to engage silent genes, helping to endow competence for cell-type specification. FoxA proteins can bind their target sites in highly compacted chromatin and open up the local region for other factors to bind; hence, they have been termed “pioneer factors.” We recently found that FoxA proteins remain bound to chromatin in mitosis, as an epigenetic mark. In embryonic stem cells, which lack FoxA, FoxA target sites can be occupied by FoxD3, which in turn helps to maintain a local demethylation of chromatin. By these means, a cascade of Fox factors helps to endow progenitor cells with the competence to activate genes in response to tissue-inductive signals. Understanding such epigenetic mechanisms for transcriptional competence coupled with knowledge of the relevant signals for cell-type specification should greatly facilitate efforts to predictably differentiate stem cells to liver and pancreatic fates.