With an estimate of 9,600 described extant species, seaweeds are a diverse and taxonomically challenging group of eukaryotes. Seaweed systematics has come a long way, and represents a vast body of work that has accumulated over the past two and a half centuries. Advances in seaweed taxonomy have often been accompanied by technological or analytical progress, including improved microscopy and culture techniques. Unquestionably, the main revolution in recent decades has come with the application of molecular data, which has profoundly reshaped our understanding of algal diversity and relationships. However, this progress has not been uniform geographically. New methods have also created taxonomic challenges, such as how to deal with cryptic diversity, non-monophyly, and old taxon names. The field of seaweed systematics is transitioning into the genomic era, which will provide further insights into diversity and classification. A second ongoing revolution comes with digital access to collections. Herbarium specimens have long been the cornerstone of taxonomic research. Their digitization is increasing access and is transforming them into new dynamic digital research tools. Digital collections likely will be targeted by machine learning for automated species discovery and delimitation. Together with other digital sources such as literature and DNA sequences, Linked Open Data will further revolutionize the way taxonomic data is managed, shared, and integrated.