The human genome is copied with high fidelity every cell cycle by the machinery of DNA replication, which initiates through the licensing and differential firing of origins of replication. Unlike in yeast, human origin firing is not determined by a sequence motif, but by a variety of factors including local epigenetic context. As a result, human replication occurs through a cell-type specific pattern of DNA replication timing, which is well correlated with, but distinct from, various genomic properties such as mutation rate and gene density. Understanding the factors underlying this program is crucial to interrogating its relationship to other aspects of the genome. While the cell type specificity of replication timing suggests a strong epigenetic component, little is understood about how variation in epigenetic states impacts the temporal pattern of replication. Here, I leverage multiple unique human stem cell systems to investigate the impact of epigenetic alterations on replication timing. I first profile DNA replication timing in haploid human embryonic stem cells (ESCs) and illustrate that increased X chromosome dosage in these haploid cells causes specific delays in autosomal replication timing which may impact their cell cycle progression. I further show that this increased X chromosome dosage can also arise via the loss of X inactivation in diploid embryonic stem cells, and similarly results in replication delays. Next, I compare patterns of ESC replication timing to two methods of stem cell reprogramming and uncover defects in the replication timing of induced pluripotent stem cells (iPSCs) compared to the ESC state. The defects occur in a subset of iPSCs, and cooccur with alterations in DNA methylation and gene expression. Finally, I examine epigenetic variation between alleles at homologous loci by profiling stem cells of uniparental origin. I illustrate parent-of-origin linked replication asynchrony between alleles at four imprinted regions. The most dramatic of these asynchronies occurs at the disease-relevant Prader-Willi Syndrome locus and spans nearly all of S-phase. I further dissect this locus by profiling patient cell lines and targeted deletions to identify potential regulators of replication timing. Together, this work identifies key relationships between epigenetics and DNA replication timing and seeks to expand our knowledge of the underpinnings of this genome-wide program.