Extrachromosomal circular DNA (eccDNA) is a closed-circle, nuclear, nonplasmid DNA molecule found in all tested eukaryotes. eccDNA plays important roles in cancer pathogenesis, evolution of tumor heterogeneity, and therapeutic resistance. It is known under many names, including very large cancer-specific circular extrachromosomal DNA (ecDNA), which carries oncogenes and is often amplified in cancer cells. Our understanding of eccDNA has historically been limited and fragmented. To provide better a context of new and previous research on eccDNA, in this review we give an overview of the various names given to eccDNA at different times. We describe the different mechanisms for formation of eccDNA and the methods used to study eccDNA thus far. Finally, we explore the potential clinical value of eccDNA.