Different parts of the United Kingdom have different rules governing pets: The chips are compulsory in Northern Ireland; Wales is considering such a move; Scotland has no such rule.
Inserting chips into animals' necks is a technique used worldwide to keep track both of domestic animals and livestock, although rules vary according to country. German shepherds can bound across Berlin chip-free, but Chihuahuas in Milan and Portuguese water dogs in Lisbon can't be caught without. In some parts of Spain, cats need chips too.
Alan Clendenning in Madrid, Victor Simpson in Rome, and David Rising in Berlin contributed to this report.
Royal Society for the Prevention of Cruelty to Animals' site on microchips: http://www.rspca.org.uk/allaboutanimals/pets/general/microchipping
Raphael Satter can be reached at: http://raphae.li/twitter