The Vatican City is the smallest state in the world by both population (<1000) and size (0.44 km2). It is not 'sovereign'. Sovereignty is held by the Holy See which is an entity in public international law. Like money, languages, religions, relationships and other agreements, some things exist by law if enough of us say they exist. These concepts take on a life that unlike human life, normally doesn't have an end date. All of us die. The relationships we create can live much longer if their flavour embeds deeply enough. The Papal States were territories directly ruled by the Pope from 754-1870. Gradually this territory was lost to the emerging Kingdom of Italy. The Vatican City became an independent state by agreement between Italy and the Holy See in 1929. The Holy See speaks for the whole Catholic Church diplomatically, even though it doesn't meet other criteria of statehood (permanent population, defined territory, stable government, and capacity to enter into relations with other states). It has diplomatic relations with 180 countries, and the Vatican estimates there are 1.2 Billion Roman Catholics worldwide.
Papal States - 1700
Foreign Relations with the Holy See