There are a number of traditionally itinerant or travelling groups in Europe who are known as "travellers" or "gypsies".
The largest of these groups are the Romani people of Indian origin who entered Europe in the 14th to 15th century; this includes the Sinti people, who are themselves the second largest group. The third largest group in Europe is the Yenish, an indigenous Germanic group.
The origins of the indigenous itinerant groups are unclear. They have been assumed to have taken up the travelling lifestyle out of necessity at some point during the Early Modern period but to not be ethnically distinct from their source population. However recent DNA testing has shown that the Irish Travellers are genetically distinct from their settled counterparts and more groups are being studied.
Many groups speak their own language or dialect (distinct from the settled population); it's often a blend of the local settled language and Romani language, even in non-Romani groups.
Indigenous Travellers in the Netherlands ("caravan dwellers" or "Woonwagenbewoner") are first mentioned in the 1879 census, although boat dwellers who practised the same professions (chair bottomers, traders, peddlers, artisans, etc) were common before then. 
A group who call themselves Reisende; i.e. indigenous Norwegian Travellers. Confusingly, this term is also used by the Tater people, the biggest population of Romani people in Norway and Sweden. Unlike the Tater people, the indigenous Norwegian Travellers are non-Roma by culture and origins, and they do not speak any form of Romani language.
The Pavee are ethnically Irish, but have a separate language and culture than the settled Irish.  They live predominantly in Ireland, the United Kingdom and the United States. Travellers refer to themselves as Minceir or Pavees in their own language or in Irish as an Lucht Siúil, meaning literally "the walking people". The term Pikey is a pejorative slang term used mainly in the United Kingdom to refer to Irish Travellers. The language of the Irish Travellers, Shelta, is mainly based on an Irish Gaelic lexicon and an English grammar. There are two dialects of this language: Gammon (or Gamin) and Cant. It has been dated back to the eighteenth century but may be older. The vast majority of Irish Travellers are Roman Catholics who maintain their traditions and culture in a close knit community of families.
In 2011 an analysis of DNA from 40 Travellers showed that Irish Travellers are a distinct Irish ethnic minority who separated from the settled Irish community at least 1000 years ago; the claim was made that they are as distinct from the settled community as Icelanders are from Norwegians.
Like other itinerant groups they have often been racially discriminated against in the past and still are today, although to a lesser extent. They were only recognised as an official ethnic group in the Republic of Ireland on March 1st, 2017.
The Quinqui or mercheros of Spain are a minority group, formerly nomadic, who share a similar way of life with the Spanish Roma. There are a few theories about their origin: they may be peasants who lost their land in the 16th century, descendants of Muslims who took to nomadism to avoid persecution, or marginalised people who have mixed with Roma. Most likely they are a mixture of all of the above. In spite of sharing persecution and mores with the Roma, the Quinqui have often set themselves apart from them.
The best known of these communities are the Romani people (also Romany, Romanies Tzigani, Rromani, and variants). The Romani are of Indo-Aryan origin and first entered Europe via the Middle East during the 14th century. They spread further through Europe during the 15th and 16th centuries, separating into various subgroups in the process.
There are multiple Gypsy and Traveller groups in Scotland: the indigenous Scottish Highland Travellers also known as Ceardannan (Scottish Gaelic which means "the craftsmen" or 'Black Tinkers') or more poetically as the "Summer Walkers", Scottish Border Gypsies (who are a Romani group), and Lowland Scottish Gypsy/Travellers, whose origins are unclear.  The English term 'Travelling People' has been adopted into contemporary Gaelic as "luchd siubhail" (people of travel) but this is a wider term covering other groups of itinerant communities within Scotland.
The Scottish Highland Travellers have their own now nearly extinct language based on Scottish Gaelic called Beurla Reagaird (or English Backwards). Highland Travellers are closely tied to their native Highlands the native Gaelic speaking population; they may follow a nomadic or a settled lifestyle. They have played an essential role in the preservation of traditional Gaelic culture. Travellers' outstanding contribution to Highland life has been as custodians of an ancient and vital Gaelic singing, storytelling and folklore tradition of great importance. It is estimated that only 2,000 Scottish Highland Travellers continue to lead their traditional lifestyle on the roads.
In German-speaking Europe, France and Wallonia, there are the Jenische or Yeniche (in German and French spelling, respectively). An early description of this group was published by Johann Ulrich Schöll in 1793.
Travelling Showpeople/Show Travellers (known in France as Forains Industriel), Circus and Bargees are Occupational Travellers. These groups formed around particular crafts and professions that required frequent mobility and usually follow a set pattern of nomadism year after year. Membership of these groups have, over the years been drawn from other communities (including, in the case of travelling funfairs and circuses, Romani people).
As a result Occupational Travellers are not defined as an ethnic group, even though they display certain common features; they tend to be insular favouring intermarriage resulting in long lineages and a strong sense of cultural homogeneity (The Showman's Guild of Great Britain and Ireland requires that applicants for membership have a parent from the Show Traveller community).
Further examples include the use of Parlyaree/Polari among Fairground Travellers in the UK and the development of unique jargons, customs and traditions  Linguistically, many Occupational Travellers in the fairground and circus worlds have cultural affinities with Romani groups, such as significant traces of the Romani language and matriarchial forms of social organisation.
separated from the settled community between 1,000 and 2,000 years ago.