The article about the original faith of the Celts is at Celtic polytheism
Celtic Reconstructionist Paganism, which is sometimes just called by its initials,  "CR", is a religion. People who belong to the religion call themselves "Celtic Reconstructionists" or "Celtic Reconstructionist Pagans".  Sometimes they just call themseleves "CRs".

The Celts were the people who lived long ago in many parts of Europe, but mainly in the countries of Ireland, Scotland, Wales, and Gaul (modern-day France). The Modern Celts are the people who live in those countries now, or whose ancestors lived there.

Like the ancient Celts did before them, CRs are polytheistic and have many gods and goddesses. They believe in spirits and ancestors, too, and they often honour them with rituals and offerings. Offerings to the spirits might be food, or songs, or poetry. CRs often learn the languages spoken by the Celts, if they do not speak them already. These languages include the Irish language, Scottish Gaelic, the Welsh language and others.

Celtic Reconstructionists are a type of Pagan Reconstructionist. Reconstructionists believe in practicing a religion that is from one culture. They are different from eclectic Pagans, who mix parts of different cultures together.

How it started
Celtic Reconstructionist Paganism (CR) started in the 1980s, when people interested in the Celts and in Paganism were looking for an authentic religion. By the 1990s there were lots of CRs. Some of them met each other at Pagan gatherings, and later more people met each other on the Internet.

The first person to write about being a "Celtic Reconstructionist Pagan" was Kym Lambert ní Dhoireann. She wrote this in the Spring, 1992 issue of Harvest Magazine. She says she got the idea for the name from Kathryn Price NicDhàna, who had also written about it. Margot Adler's 1979 book, Drawing Down the Moon has a chapter on "Pagan Reconstructionists", and Kathryn NicDhàna says this is probably where she got the idea, even though the book does not mention Celtic Reconstructionists, just other kinds.

What Celtic Reconstructionists believe, and what they do
Celtic Reconstructionists base their religion on what we know of the Ancient Celtic people's religion, and also on Celtic folklore. They focus on a particular Celtic culture, such as the Gaelic Welsh or Gaulish. Many CRs are scholars, or mystics, though many believe it's important to be both. CRs read lots of books and do things like meditation, prayer, and rituals. CRs believe that honesty and honorable behaviour is important.

Many CRs view each act of daily life as a form of ritual, and they accompany daily activities with traditional prayers, chants and songs from sources such as the Scottish Gaelic Carmina Gadelica or manuscript collections of ancient Irish or Welsh poetry.

Community rituals are usually based on traditional community celebrations found in folkloric collections by authors such as Marian McNeill, Kevin Danaher or John Gregorson Campbell. These celebrations often involve bonfires, dances, songs, divination and children's games. More formal or mystical CR rituals are often based on traditional techniques of interacting with the Otherworld, such as the act of making offerings of food, drink and art to the spirits of the land, ancestral spirits, and the Celtic deities. CR ritual structures are based on the ancient Celtic idea of the "Three Realms" - Land, Sea and Sky - with the fire of inspiration seen as a central, uniting force. Many CRs have altars and shrines to the spirits and deities they believe in.  They may place these altars at outdoor, natural locations such as wells, streams, and special trees. Some CRs practice divination, such as the taking of omens from the shapes of clouds or the behaviour of birds and animals.

Other names for Celtic Reconstructionists
While Celtic Reconstructionism was the earliest name in use, and is still used the most often, other names for a Celtic Reconstructionist approach have also come into use, with varying degrees of success.

Pàganachd / Págánacht
Some CR groups have looked to Celtic languages for a more culturally specific name for the tradition, or for their branch of the tradition. There are groups who now described their traditions as Pàganachd ("Paganism, Heathenism" in Scottish Gaelic) or the Irish version, Págánacht.  Some Gaelic-oriented groups use the two terms somewhat interchangeably, or further modify these terms to describe the CR sub-tradition practiced by their particular group, such as Pàganachd Allaidh (“Wild Paganism”)   or Pàganachd Bhandia (“Paganism of Goddesses”),
both used by Gaelic Reconstructionist groups on the East Coast of the US.

Senistrognata
In the late 1990s, members of Imbas, a Celtic Reconstructionist group in Seattle, began promoting the name Senistrognata, which they say means "the ancestral customs of the Celtic peoples"  in reconstructed Old Celtic.

Other
The Irish word for “polytheism”, Ildiachas, is in use by at least one group on the West Coast of the US as Ildiachas Atógtha (“reconstructed polytheism”).
Aurrad, which came into use among members of the Nemeton mailing list in the mid 1990s, means "person of legal standing in the túath" in Old Irish.

Related pages
Celt
Celtic mythology
Celtic polytheism
Modern Celts
Polytheistic Reconstructionism
 Festivals
Imbolc
Beltane
Lughnasadh
Samhain

References

More reading

Celtic Reconstructionism
Adler, Margot (1979) Drawing Down the Moon: Witches, Druids, Goddess-Worshippers, and Other Pagans in America Today
Bonewits, Isaac (2006) Bonewits's Essential Guide to Druidism. New York, Kensington Publishing Group  Chapter 9: "Celtic Reconstructionists and other Nondruidic Druids"
Fairgrove, Rowan (1994) What we don't know about the ancient Celts. Originally printed in The Pomegranate, 2. Now available online
Kondratiev, Alexei (1998) The Apple Branch: A Path to Celtic Ritual. San Francisco, Collins.  (1st edition),  (2nd edition) [also reprinted without revision under the title Celtic Rituals]
Laurie, Erynn Rowan (1995) A Circle of Stones: Journeys and Meditations for Modern Celts. Chicago, Eschaton. 
McColman, Carl (2003) The Complete Idiot's Guide to Celtic Wisdom. Alpha Press 
NicDhàna, Kathryn Price; Erynn Rowan Laurie, C. Lee Vermeers, Kym Lambert ní Dhoireann, et al. (2007) The CR FAQ - An Introduction to Celtic Reconstructionist Paganism. River House Publishing. 
Telesco, Patricia [editor] (2005) Which Witch is Which? Franklin Lakes, NJ, New Page Books / The Career Press , p. 85-9: "Celtic Reconstructionist Paganism"

Celtic polytheism and folklore

Celtic Reconstructionists rely on primary mythological texts, as well as surviving folklore, for the basis of their religious practices. No list can completely cover all the recommended works, but this is a small sample of sources used.

General Celtic
Evans Wentz, W. Y. (1966, 1990) The Fairy-Faith in Celtic Countries. Gerrards Cross, Colin Smythe Humanities Press 
MacCana, Proinsias (1970) Celtic Mythology. Middlesex, Hamlyn. 
MacKillop, James (1998) A Dictionary of Celtic Mythology. Oxford, Oxford University Press. 
Rees, Alwyn and Brinley (1961) Celtic Heritage: Ancient Tradition in Ireland and Wales. New York, Thames and Hudson. 
Sjoestedt, Marie-Louise (1982) Gods and Heroes of the Celts. Translated by Myles Dillon, Berkeley, CA, Turtle Island Foundation. 

Gaelic (Irish and Scottish)
Campbell, John Gregorson (1900, 1902, 2005) The Gaelic Otherworld.  Edited by Ronald Black. Edinburgh, Birlinn Ltd. 
Carmichael, Alexander (1992) Carmina Gadelica: Hymns and Incantations (with illustrative notes on wards, rites, and customs dying and obsolete/ orally collected in the highlands and islands of Scotland by Alexander Carmichael). Hudson, NY, Lindisfarne. 
Clark, Rosalind (1991) The Great Queens: Irish Goddesses from the Morrigan to Cathleen ni Houlihan. Savage, MD, Barnes and Noble Books. 
Danaher, Kevin (1972) The Year in Ireland.  Dublin, Mercier. 
Dillon, Myles (1994) Early Irish Literature. Dublin, Four Courts Press. 
Gray, Elizabeth A (1982) Cath Maige Tuired: The 2nd Battle of Mag Tuired. Dublin, Irish Texts Society
McNeill, F. Marian (1959). The Silver Bough, Vol. 1-4.  Glasgow, William MacLellan
Nagy, Joseph Falaky (1985) The Wisdom of the Outlaw: The Boyhood Deeds of Finn in Gaelic Narrative Tradition. Berkely, University of California Press. 
Patterson, Nerys Thomas (1994) Cattle Lords and Clansmen: The Social Structure of Early Ireland. Notre Dame, IN, University of Notre Dame Press (2nd edition) 
Power, Patrick C. (1976) Sex and Marriage in Ancient Ireland. Dublin, Mercier
Smyth, Daragh (1988, 1996) A Guide to Irish Mythology. Dublin, Irish Academic Press

Comparative European
Davidson, H.R. Ellis (1988) Myths and Symbols in Pagan Europe: Early Scandinavian and Celtic Religions. Syracuse, Syracuse University Press. 
Epstein, Angelique Gulermovich (1998) War Goddess: The Morrígan and Her Germano-Celtic Counterparts. Los Angeles, University of California
Lincoln, Bruce (1991) Death, War, and Sacrifice: Studies in Ideology and Practice. Chicago, University of Chicago Press.

Other websites
The CR FAQ - An Introduction to Celtic Reconstructionist Paganism: Written by representatives of different CR groups - including some of the founders of the tradition - the FAQ is only the second document to present a consensus view that speaks for more than one group's vision.
Celtic Reconstructionist Paganism : The much-briefer consensus tradition statement from 2003. Contains unclear bits that were later cleared up in the FAQ, but a much quicker read than the FAQ.
What we mean by Celtic Reconstructionism : Statement from Imbas

Organisations
Dùn Sgàthan  (New Hampshire)
Gaol Naofa: Gaelic Polytheism Organisation (Florida)
IMBAS  (Seattle, Washington)
New Tara : Diverse Celtic group which includes Reconstructionists (Toronto)
Macalla : Núcleo de Estudos e Pesquisas Celtas (Rio de Janeiro, Brazil)

Online portals
CAORANN: Celts Against Oppression, Racism and Neo-Nazism
Pàganachd / Págánacht: Home of the CR FAQ and other CR resources.
 Tres Mundos : Paganismo Reconstrucionista Celta (Portuguese)

Paganism