To date (1 November 2023), the online database AlgaeBase has documented 50,589 species of living algae and 10,556 fossil species here referred to four kingdoms (Eubacteria, Chromista, Plantae, and Protozoa), 14 phyla, and 63 classes. The algae are the third most speciose grouping of plant‐like after the flowering plants (≈382,000 species) and fungi (≈170,000 species, including lichens) but are the least well defined of all the botanical groupings. Priority is given to phyla and class names that are familiar to phycologists and that are nomenclaturally valid. The most species‐rich phylum is the Heterokontophyta to which 18 classes are referred with 21,052 living species and which is dominated by the diatoms in three classes with 18,673 species (16,427 living; 2239 fossil). The next most species‐rich phyla are the red algae (7276 living), the green algae (6851 living), the blue‐green algae (Cyanobacteria, 5723 living), the charophytes (4950 living, including the Charophyceae, 511 species living, and the Zygnematophyceae, 4335 living species), Dinoflagellata (2956 living, including the Dinophyceae, 2828 extant), and haptophytes (Haptophyta 1722 species, 517 living).