Among all economically important plant species in the world, grapevine (Vitis vinifera L.) is the most cultivated fruit plant. It has a significant impact on the economies of many countries through wine and fresh and dried fruit production. In recent years, the grape and wine industry has been facing outbreaks of known and emerging viral diseases across the world. Although high-throughput sequencing (HTS) has been used extensively in grapevine virology, the application and potential of third-generation sequencing have not been explored in understanding grapevine viruses and their impact on the grapevine. Nanopore sequencing, a third-generation technology, can be used for the direct sequencing of both RNA and DNA with minimal infrastructure. Compared to other HTS methods, the MinION nanopore platform is faster and more cost-effective and allows for long-read sequencing. Due to the size of the MinION device, it can be easily carried for field viral disease surveillance. This review article discusses grapevine viruses, the principle of third-generation sequencing platforms, and the application of nanopore sequencing technology in grapevine virus detection, virus–plant interactions, as well as the characterization of viral RNA modifications.