Travel by EU Citizens making use of EU treaty rights related to freedom of movement. This is distinict from visa-free travel which normally is at the discretion of the country enterting - permission to enter is protected under EU Law.
The summary on EU-Lex says:
European Union citizens have the right to move freely and live in another EU country, subject to any conditions set out in the EU’s treaties. This free movement of people is one of the EU’s fundamental principles.
EU citizens with a valid identity card or passport may:
- Enter another EU country, as may their family members - whether EU citizens or not - without requiring an exit or entry visa.
- Live in another EU country for up to 3 months without any conditions or formalities.
- Live in another EU country for longer than 3 months subject to certain conditions, depending on their status in the host country. Those who are employed or self-employed do not need to meet any other conditions. Students and other people not working for payment, such as those in retirement, must have sufficient resources for themselves and their family, so as not to be a burden on the host country’s social assistance system, and comprehensive sickness insurance cover.
- Have to register with the relevant authorities if living in the country longer than 3 months. Their family members, if not EU nationals, require a residence card valid for 5 years.
- Be entitled to permanent residence if they have lived legally in another EU country for a continuous period of 5 years. This also applies to family members.
- Have the right to be treated on an equal footing with nationals of the host country. However, host authorities are not obliged to grant benefits to EU citizens not working for payment during the first 3 months of their stay.