Historically, bacteria were first classified as plants constituting the class Schizomycetes, which along with the Schizophyceae (blue-green algae/Cyanobacteria) formed the phylum Schizophyta, then in the phylum Monera in the kingdom Protista by Haeckel in 1866, comprising Protogens, Protamaeba, Vampyrella, Protomonae, and Vibrio, but not Nostoc and other cyanobacteria, which were classified with algae, later reclassified as the Prokaryotes by Chatton.
The cyanobacteria were traditionally classified by morphology into five sections, referred to by the numerals I–V. The first three – Chroococcales, Pleurocapsales, and Oscillatoriales – are not supported by phylogenetic studies. The latter two – Nostocales and Stigonematales – are monophyletic as a unit, and make up the heterocystous cyanobacteria.
The members of Chroococales are unicellular and usually aggregate in colonies. The classic taxonomic criterion has been the cell morphology and the plane of cell division. In Pleurocapsales, the cells have the ability to form internal spores (baeocytes). The rest of the sections include filamentous species. In Oscillatoriales, the cells are uniseriately arranged and do not form specialized cells (akinetes and heterocysts). In Nostocales and Stigonematales, the cells have the ability to develop heterocysts in certain conditions. Stigonematales, unlike Nostocales, include species with truly branched trichomes.
Most taxa included in the phylum or division Cyanobacteria have not yet been validly published under The International Code of Nomenclature of Prokaryotes (ICNP) except:
*The classes Chroobacteria, Hormogoneae, and Gloeobacteria
*The orders Chroococcales, Gloeobacterales, Nostocales, Oscillatoriales, Pleurocapsales, and Stigonematales
*The families Prochloraceae and Prochlorotrichaceae
*The genera Halospirulina, Planktothricoides, Prochlorococcus, Prochloron, and Prochlorothrix
The remainder are validly published under the International Code of Nomenclature for algae, fungi, and plants.
Formerly, some bacteria, like Beggiatoa, were thought to be colorless Cyanobacteria.
The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI).
Class "Cyanobacteriia"
* Subclass "Gloeobacteria" 
** Gloeobacterales 
* Subclass "Phycobacteria" 
** Acaryochloridales  [incl. Thermosynechococcales]
** Aegeococcales 
** "Elainellales" 
** "Eurycoccales" 
** Geitlerinematales 
** Gloeoemargaritales 
** "Leptolyngbyales" 
** Nodosilineales 
** Oculatellales 
** "Phormidesmiales" 
** Prochlorococcaceae  {"PCC-6307"}
** Pseudanabaenales 
** "Pseudophormidiales" 
** Thermostichales 
** Synechococcophycidae 
*** "Limnotrichales" 
*** Prochlorotrichales  (PCC-9006)
*** Synechococcales 
** Nostocophycidae 
*** Cyanobacteriales  (Chamaesiphonales, Chroococcales, Chroococcidiopsidales, Nostocales, Oscillatoriales, Pleurocapsales, Spirulinales, Stigonematales)