Circular forms of RNA were first discovered in plant viroids and later found in a variety of animal viruses. These circular RNAs lack free 5′ and 3′ ends, granting protection from exonucleases. This review is focused on the methods that are used to investigate virus-encoded circular RNAs. Using DNA viruses that are prevalent among human as examples, we begin with features of circular RNAs and the unique methods to enrich for circular RNAs. Next, we discuss the computational methods for RNA-sequencing analysis to discover new virus-encoded circular RNAs. Many strategies are similar to analyzing cellular RNAs, but some unique aspects of virus-encoded circular RNAs that are likely due to highly packed viral genomes and non-canonical use of splicing machinery, are described herein. We illustrate the various methods of validating expression of specific virus-encoded circular RNAs. Finally, we discuss novel methods to study functions of circular RNAs and the current technical challenges that remain for investigating virus-encoded circular RNAs.