There is no restriction to live and work in Greece for EU national but non EU citizens must apply for permission.
Resident permits are now only a formality for EU citizens, although non-working residents must have sufficient income to maintain themselves while living in Greece.
Visitors can stay for 3 months without any formalities but if someone wants to stay longer, open a business or purchase a car in Greece a resident permit is still required
Work permits are no longer necessary for EU nationals to work in Greece.