Faithful replication of the DNA is critical for cell proliferation and genome stability. In eukaryotes, initiation and progression of DNA replication is highly organized in both space and time. The spatiotemporal DNA replication timing program can be observed as fluctuations in local DNA copy number measured by whole-genome sequencing, and is associated with genomic features including gene expression, nucleotide composition, and chromatin state. However, it remains unclear what regulatory mechanisms underlie the high reproducibility of replication timing assays. Any such mechanism must be able to explain the range of replication timing variation observed; this dissertation characterizes such variation in human replication timing in two distinct contexts. First, I use two new human reference genome assemblies to characterize replication timing variation in genomic regions with high satellite DNA content. These repeat-rich regions are difficult to assemble and have historically been excluded from replication timing analysis. I focus initially on centromeres, and then expand the analysis to constitutive heterochromatin. I find that these regions are biased toward replication in late S phase and appear to have similar replication timing structure to other better- characterized regions of the genome. Of particular interest, I find that some human cell lines replicate the centromeric regions earlier in S phase than others and that this trend is consistent across all chromosomes for a given cell line, suggesting that centromeric replication may be coordinate genome-wide. Second, I examine replication timing variation at the single-cell level, across cell lines and cell types. I describe an in silico cell sorting strategy for identifying replicating cells based on single-cell DNA sequencing and analyze replication timing for up to 2,437 cells from a single cell line. I find that sites of replication initiation are shared across cells. The timing of initiation at those sites is predicted by their ensemble replication timing, although all initiation sites fire at an unexpected time during S phase in some fraction of cells. In particular, late-replicating regions contain previously unappreciated heterogeneity in initiation behavior, including initiation sites that are early- replicating but infrequently used. Together, these studies describe underexplored aspects of variation that ought to be accounted for in models of DNA replication regulation.