The photosynthetic organelle of algae and plants (the plastid) traces its origin to a primary endosymbiotic event in which a previously non-photosynthetic protist engulfed and enslaved a cyanobacterium. This eukaryote then gave rise to the red, green and glaucophyte algae. However, many algal lineages, such as the chlorophyll c-containing chromists, have a more complicated evolutionary history involving a secondary endosymbiotic event, in which a protist engulfed an existing eukaryotic alga (in this case, a red alga). Chromists such as diatoms and kelps then rose to great importance in aquatic habitats. Another algal group, the dinoflagellates, has undergone tertiary (engulfment of a secondary plastid) and even quaternary endosymbioses. In this review, we examine algal diversity and show endosymbiosis to be a major force in algal evolution. This area of research has advanced rapidly and long-standing issues such as the chromalveolate hypothesis and the extent of endosymbiotic gene transfer have recently been clarified.