One of the most fascinating and unusual features of trypanosomatids, parasites that cause disease in many tropical countries, is their mitochondrial DNA. This genome, known as kinetoplast DNA (kDNA), is organized as a single, massive DNA network formed of interlocked DNA rings. In this review, we discuss recent studies on kDNA structure and replication, emphasizing recent developments on replication enzymes, how the timing of kDNA synthesis is controlled during the cell cycle, and the machinery for segregating daughter networks after replication.