Algae are photosynthetic organisms that drive aquatic ecosystems, e.g. fuelling food webs or forming harmful blooms. The discovery of viruses that infect eukaryotic algae has raised many questions about their influence on aquatic primary production and their role in algal ecology and evolution. Although the full extent of algal virus diversity is still being discovered, this review summarizes current knowledge of this topic. Where possible, formal taxonomic classifications are referenced from the International Committee on Taxonomy of Viruses (ICTV); since the pace of virus discovery has far surpassed the rate of formal classification, however, numerous unclassified viruses are discussed along with their classified relatives. In total, we recognized 61 distinct algal virus taxa with highly variable morphologies that include dsDNA, ssDNA, dsRNA, and ssRNA genomes ranging from approximately 4.4 to 560 kb, with virion sizes from approximately 20 to 210nm in diameter. These viruses infect a broad range of algae and, although there are a few exceptions, they are generally lytic and highly species or strain specific. Dedicated research efforts have led to the appreciation of algal viruses as diverse, dynamic, and ecologically important members of the biosphere, and future investigations will continue to reveal the full extent of their diversity and impact.