A concordat is an agreement between the Holy See of the Catholic Church and a sovereign state on religious matters. Legally, it is an international treaty. Concordats often include both recognition and privileges for the Catholic Church in a particular country. Privileges might include exemptions from certain legal matters and processes, and issues such as taxation as well as the right of a state to influence the selection of bishops within its territory.
The Council of Constance proclaimed the Concordat to be the regular form of governing relations between the Papacy and foreign kingdoms.
Although for a time after the Second Vatican Council, which ended in 1965, the term 'concordat' was dropped, it reappeared with the Polish Concordat of 1993 and the Portuguese Concordat of 2004. A different model of relations between the Vatican and various states is still evolving (see e.g. Petkoff 2007) in the wake of the Second Vatican Council's Declaration on Religious Liberty, Dignitatis Humanae.