Eukaryotic cells must accurately and efficiently duplicate their genomes during each round of the cell cycle. Multiple linear chromosomes, an abundance of regulatory elements, and chromosome packaging are all challenges that the eukaryotic DNA replication machinery must successfully overcome. The replication machinery, the “replisome” complex, is composed of many specialized proteins with functions in supporting replication by DNA polymerases. Efficient replisome progression relies on tight coordination between the various factors of the replisome. Further, replisome progression must occur on less than ideal templates at various genomic loci. Here, we describe the functions of the major replisome components, as well as some of the obstacles to efficient DNA replication that the replisome confronts. Together, this review summarizes current understanding of the vastly complicated task of replicating eukaryotic DNA.