information:extraction, structural:summarization, structural:reformatting
Classifications

One definition of algae is that they "have chlorophyll as their primary photosynthetic pigment and lack a sterile covering of cells around their reproductive cells ". On the other hand, the colorless Prototheca under Chlorophyta are all devoid of any chlorophyll. Although cyanobacteria are often referred to as "blue-green algae", most authorities exclude all prokaryotes, including cyanobacteria, from the definition of algae.

The algae contain chloroplasts that are similar in structure to cyanobacteria. Chloroplasts contain circular DNA like that in cyanobacteria and are interpreted as representing reduced endosymbiotic cyanobacteria. However, the exact origin of the chloroplasts is different among separate lineages of algae, reflecting their acquisition during different endosymbiotic events. The table below describes the composition of the three major groups of algae. Their lineage relationships are shown in the figure in the upper right. Many of these groups contain some members that are no longer photosynthetic. Some retain plastids, but not chloroplasts, while others have lost plastids entirely.

Phylogeny based on plastid not nucleocytoplasmic genealogy:

Linnaeus, in Species Plantarum (1753), the starting point for modern botanical nomenclature, recognized 14 genera of algae, of which only four are currently considered among algae. In Systema Naturae, Linnaeus described the genera Volvox and Corallina, and a species of Acetabularia (as Madrepora), among the animals.

In 1768, Samuel Gottlieb Gmelin (1744–1774) published the Historia Fucorum, the first work dedicated to marine algae and the first book on marine biology to use the then new binomial nomenclature of Linnaeus. It included elaborate illustrations of seaweed and marine algae on folded leaves.

W. H. Harvey (1811–1866) and Lamouroux (1813) were the first to divide macroscopic algae into four divisions based on their pigmentation. This is the first use of a biochemical criterion in plant systematics. Harvey's four divisions are: red algae (Rhodospermae), brown algae (Melanospermae), green algae (Chlorospermae), and Diatomaceae.

At this time, microscopic algae were discovered and reported by a different group of workers (e.g., O. F. Müller and Ehrenberg) studying the Infusoria (microscopic organisms). Unlike macroalgae, which were clearly viewed as plants, microalgae were frequently considered animals because they are often motile. Even the nonmotile (coccoid) microalgae were sometimes merely seen as stages of the lifecycle of plants, macroalgae, or animals.

Although used as a taxonomic category in some pre-Darwinian classifications, e.g., Linnaeus (1753), de Jussieu (1789), Lamouroux (1813), Harvey (1836), Horaninow (1843), Agassiz (1859), Wilson & Cassin (1864), in further classifications, the "algae" are seen as an artificial, polyphyletic group.

Throughout the 20th century, most classifications treated the following groups as divisions or classes of algae: cyanophytes, rhodophytes, chrysophytes, xanthophytes, bacillariophytes, phaeophytes, pyrrhophytes (cryptophytes and dinophytes), euglenophytes, and chlorophytes. Later, many new groups were discovered (e.g., Bolidophyceae), and others were splintered from older groups: charophytes and glaucophytes (from chlorophytes), many heterokontophytes (e.g., synurophytes from chrysophytes, or eustigmatophytes from xanthophytes), haptophytes (from chrysophytes), and chlorarachniophytes (from xanthophytes).

With the abandonment of plant-animal dichotomous classification, most groups of algae (sometimes all) were included in Protista, later also abandoned in favour of Eukaryota. However, as a legacy of the older plant life scheme, some groups that were also treated as protozoans in the past still have duplicated classifications (see ambiregnal protists).

Some parasitic algae (e.g., the green algae Prototheca and Helicosporidium, parasites of metazoans, or Cephaleuros, parasites of plants) were originally classified as fungi, sporozoans, or protistans of incertae sedis, while others (e.g., the green algae Phyllosiphon and Rhodochytrium, parasites of plants, or the red algae Pterocladiophila and Gelidiocolax mammillatus, parasites of other red algae, or the dinoflagellates Oodinium, parasites of fish) had their relationship with algae conjectured early. In other cases, some groups were originally characterized as parasitic algae (e.g., Chlorochytrium), but later were seen as endophytic algae. Some filamentous bacteria (e.g., Beggiatoa) were originally seen as algae. Furthermore, groups like the apicomplexans are also parasites derived from ancestors that possessed plastids, but are not included in any group traditionally seen as algae.