Bl. Pope Gregory X reigned from 1271 to 1276.
Pope Celestine I
Pope John XXIII convened the Council and Pope Paul VI made the changes to the Mass.
Pope John XXIII called for the council and Pope Paul VI continued it after he was elected pope in 1963.
Pope Paul III called for the council.
They are two Popes: John the 23 during 1960-63 and Pope Paul 6 to 1965.
Pope Pius IX convened the First Vatican Council which began in 1868. Pope John XXIII convened the Second Vatican Council which began in 1962. Pope Paul VI reconvened the Second Vatican Council in 1963 after it was suspended due to the death of Pope John. Pope John had to close the First Vatican Council before opening the Second Council since the First Council was never officially closed by Pius, it ended abruptly, or temporarily suspended because the Franco-Prussian War broke out and the bishops in attendance wanted to return to their diocese. After Rome was captured, Pope Pius permanently suspended the Council but did not close it officially. Pope John died during the intermission break between the first and second session of the Second Council to which it was suspended. Once Cardinal Giovanni Montini was elected as Pope Paul VI, he reconvened the Second Council and presided over it until its ending in 1965.
Pope John XXIII called the council and Pope Paul VI continued it in his reign.
Popes John XXIII and Paul VI were popes during Vatican II.
Pope Urban II
As of 30 May 2014 there have been two named saints from the Second Vatican Council. Pope St. John XXIII was the pope that called the Council, and Pope St. John Paul II was a participant in the Council.
Pope Paul III convened the Council of Trent in 1545.
Pope John XXIII called for the council and opened it. However, he died before it ended and it was closed by Pope Paul VI.