This is a taxonomy of the Kingdom Rhodophytae.  In general this follows the system of Saunders and Hommersand (2004) in which the group has two phyla, Rhodophyta and Cyanidiophyta.  I have added the Glaucophyta as a group with incertae sedis.

PHYLUM RHODOPHYTA

SUBPHYLUM RHODELLOPHYTINA

  CLASS RHODELLOPHYCEAE

ORDER RHODELLIALES (Called Porphyridiales 1 in Saunders and Hommersand, 2004).

Rhodella, Dixoniella, Glaucosphaera

ORDER STYLONEMATALES (Called Porphyridiales 2 in Saunders and Hommersand, 2004).

Stylonema, Bangiopsis, Chroodactylon, Chroothece, Goniotrichopsis, Rhodosorus

ORDER PORPHYRIDIALES (Called Porphyridiales 3 in Saunders and Hommersand, 2004).

Porphyridium, Flintiella

SUBPHYLUM METARHODOPHYTINA

  CLASS COMSPOPOGONOPHYCEAE

SUBPHYLUM EURHOPHYTINA

  CLASS BANGIOPHYCEAE

ORDER BANGIALES 

Bangia, Porphyra, Porphyrella.

  CLASS FLORIDEOPHYCEAE

    SUBCLASS HILDENBRANDIOPHYCIDAE

ORDER HILDENBRANDIALES

Hildenbrandia

    SUBCLASS NEMALIOPHYCIDAE

ORDER NEMALIALES

Nemalion, Liagora, Pseudogloiophloea, Galaxaura, Kylinia, Cumagloia.

ORDER ACROCHAETIALES

Acrochaetium, Audouinella, Rhodochorton, Yamadaella.

ORDER BALBIANIALES

Balbiana.

ORDER BALLIALES

Ballia.

ORDER BATRACHOSPERMALES

Batrachospermum, Lemanea, Sirodotia.

ORDER COLACONEMATALES

Colaconema.

ORDER CORALLINALES

Corallina, Bossiella, Calliathron, Choreonema, Jania, Lithoporella, Lithothamnium, Lithothrix, Phymatolithon, Porolithon, Sporolithon, Kvaleya, Amphiroa, Melobesia, Clathromorphum.

ORDER PALMERIALES

Palmaria, Halosaccion, Rhodophysema. Camontagnea.

ORDER RHODOGORGONALES

Rhodogorgon, Renouxia.

ORDER THOREALES

Thorea.

    SUBCLASS AHNFELDTOPHYCIDAE

ORDER AHNFELTIALES

Ahnfeltia, Gymnogongrus, Phyllophora, Stenogramme.

ORDER PIHIELLALES

Pihiella.

    SUBCLASS RHODYMENIOPHYCIDAE

ORDER RHODYMENIALES

Rhodymenia, Botryocladia, Chrysymenia, Coelarthrum, Coelothrix, Fauchia, Halosaccion, Champia, Chylocladia, Coeloseira, Gasstroclonium, Lomentaria.

ORDER BONNEMAISONIALES

Asparagopsis, Bonnemaisonia, Delisia, Ptilonia.

ORDER CERAMIALES

Ceramium, Aristothamnion, Bornetia, Compsothamnion, Corynospora, Crouania, Dohrniella, Ptilota, Griffithsia, Pleonosporium, Plumaria, Ptilothamniopsis, Seirospora, Spermothamnion, Tiffaniella, Callithamnion, Antithamnion, Bostrychia, Chondria, Colacopsis, Lenormandia, Heterosiphonia, Dasya, Platysiphonia, Membranoptera, Delesseria, Caloglossa, Phycodrys, Polyneura, Polysiphonia, Petrosiphonia, Amplisiphonia, Rhodomela, Rytiphlaea, Vidalia, Laurencia, Cryptopleura, Hemineura, Hypoglossum, Martensia, Nitophyllum, Rhodoptilum.

ORDER GELIDIALES

Gelidium, Pterocladia, Suhria.

ORDER GIGARTINALES

Gigartina, Acrosymphyton, Dumontia, Mastocarpus, Chondrus, Iridaea, Phyllophora, Gymnogongrus, Cruoria, Cruoriopsis, Pterocoelis, Bertholdia, Furcellaria, Halarachnion, Neurocaulon, Rhodophyllis, Cystoclonium, Calliblepharis, Polyides, Besa, Neoardhiella, Opuntiella, Euchemia, Gracilaria, Gracilariophila.

ORDER GRACILARIALES

Gracilaria, Gracilariopsis, Gracilariophila, Hydropuntia.

ORDER HALYMENIALES

Cryptonemia, Grateloupia, Halymenia, Lobocolax, Pachymeniopsis, Prionitis, Sebdenia.

ORDER NEMASTOMATALES

Nemastoma, Platoma, Schizymenia

ORDER PLOCAMIALES

Pliocamium, Pseudoanemonia, Sarcodia

ORDER RHODYMENIALES

Champia, Fauchea, Lomentaria, Rhodymenia.

PHYLUM CYANIDIOPHYTA

  CLASS CYANIDIOPHYCEAE

ORDER CYANIDIALES

Cyanidium, Cyanidioschyzon, Galdieria.

INCERTAE SEDIS:

PHYLUM CLAUCOPHYTA

  CLASS GLAUCOCYSTOPHYCEAE

ORDER GLAUCOSYSTIDALES

Glaucocystis, Cyanophora, Gloeochaete, Glaucosphaera.