During his pontificate, repeated difficulties with Louis XIV led to the temporary loss of Avignon and acceptance of the humiliating terms of the treaty of Pisa in 1664.
Alexander fought Jansenism by compelling the Frenchclergy to sign his "formulary."
Supported Venice in their fight with the expanding Turks.
He was a patron of art, beautified Rome and many of its churches, enlarged the libraries of the Vatican and the Roman University, and befriended men of letters.