Tissue-specific progenitor cells emerge during development to expand and differentiate into the multiple cell lineages that populate the embryo. Appropriate differentiation of these precursor cells requires coordinated expression of numerous lineage-specific genes and repression of alternative fate programs. Epigenetic regulators are enzymes capable of activating or silencing large genomic domains by altering histone modifications, DNA methylation status and chromatin organization. Although differentiating progenitor cells undergo epigenetic changes and epigenetic factors are required for appropriate cell behavior, the precise mechanism of how these proteins influence cell fate remains unclear. In this dissertation, I examine the role of histone deacetylase 3 in control of neural crest and cardiac progenitor cell commitment. Using Cre-mediated genetic deletion, I generated tissue-specific mouse models to study the function of Hdac3 in both neural crest and cardiac cells. These studies revealed a critical role for Hdac3 in maintaining neural crest proliferation and cell survival through regulation of a core network of factors required for craniofacial development. In cardiac progenitors, Hdac3 maintains appropriate differentiation into the cardiomyocyte, smooth muscle and endothelial cell lineages that make up the developed heart. Hdac3 represses a cardiomyocyte-specific gene program and prevents precocious differentiation of progenitors into the myocyte lineage. Surprisingly, this protein does not require deacetylase activity to repress myocyte commitment, and instead serves as a tether to retain myocyte-specific genomic loci at the nuclear periphery. This novel mechanism of gene repression and lineage specification highlights the role that nuclear architecture plays in controlling transcriptional activity and progenitor cell behavior.