Just as before, you will need a passport to travel to the EU. However, your passport will now need to be valid for at least 6 months from your departure date. Your passport will also need to be less than 10 years old, no matter how long it is valid for.
British and Irish citizens travelling between Great Britain and Ireland can use a form of official photographic ID or a birth certificate (for under 18's with no photo ID) instead of a passport.