|Bishop of Rome|
|Papacy began||12 December 1254|
|Papacy ended||25 May 1261|
|Created cardinal||18 September 1227|
by Gregory IX
|Birth name||Rinaldo di Jenne|
|Born||1199 or c. 1185|
Jenne, Papal States
|Died||25 May 1261|
Viterbo, Papal States
|Coat of arms|
|Other popes named Alexander|
He was born as Rinaldo di Jenne in Jenne (now in the Province of Rome), he was, on his mother's side, a member of the family de' Conti di Segni, the counts of Segni, like Pope Innocent III and Pope Gregory IX. His uncle Gregory IX made him cardinal deacon and Protector of the Order of Franciscans in 1227, Camerlengo of the Holy Roman Church from 1227 until 1231 and Bishop of Ostia in 1231 (or 1232). He became Dean of the College of Cardinals in 1244 (or 1240). On the death of Pope Innocent IV in 1254 he was elected pope at Naples on 12 December 1254.
Alexander's pontificate was signaled by efforts to reunite the Eastern Orthodox churches with the Catholic Church, by the establishment of the Inquisition in France, by favours shown to the mendicant orders, and by an attempt to organize a crusade against the Tatars after the second raid against Poland in 1259.
On 26 September 1255, Alexander IV canonized Saint Clare of Assisi (Santa Chiara in Italian), founder of the religious order for women called the Poor Clares. On 29 October 1255, in the papal bull Benigna Operatio, Alexander declared "his own knowledge" of the stigmata attributed to Saint Francis of Assisi.
In 1256, Alexander IV condemned theories of Joachim of Fiore, a millenarian prophet who had died in 1202 and whose ideas were taken up by the Fraticelli strand of the Franciscan Order. On the basis on his interpretation of the Book of Revelation, Joachim had postulated that 1260 would see the beginning of a Third Age, an age governed by the Holy Spirit, in which the hierarchy of the Church would become unnecessary - an idea which was obviously unwelcome to the Pope. In the event, 1260 - still in Alexander IV 's lifetime - came and went with no such Third Age materializing, but Joachim's ideas would in later centuries be taken up by the Cult of the Holy Spirit which had a major impact in Portugal and its colonies.
The pontiff also, on 27 September 1258, declared in the bull Quod super nonnullis that "divination or sorcery" was not to be investigated by Inquisitors of the Church, who were tasked with investigating heresy. Crimes involving magic should be left to local authorities unless they had "knowledge of manifest heresy to be involved", wherein "manifest heresy" included "praying at the altars of idols, to offer sacrifices, to consult demons, [or] to elicit responses from them". At this period in Church history, the use of magic was not seen as inherently heretical, but rather rooted in superstition or erroneous beliefs. 
On 14 May 1254, shortly before his death, Innocent IV had granted Sicily, a papal fiefdom, to Edmund, second son of King Henry III of England. Alexander confirmed the grant on 9 April 1255, in return for 2000 ounces of gold per annum, the service of 300 knights for three months when required, and 135,541 marks to reimburse the pope for the money he had expended attempting to oust Manfred from Sicily. Henry's unsuccessful attempts to persuade his subjects to pay the taxes required to meet Alexander's demands were one of the factors in the conflict between the king and parliament which culminated in the Second Barons' War. On 12 April 1261, shortly before his death, Alexander issued a papal bull for King Henry that absolved him and the magnates of his realm from the oaths taken in the Provisions of Oxford, which was instrumental in the War.
Alexander IV succeeded Innocent IV as guardian of Conradin, the last of the Hohenstaufens, promising him protection; but in less than three weeks he conspired against him and bitterly opposed Conradin's uncle Manfred. Alexander IV threatened excommunication and interdict against the party of Manfred without effect. Nor could he enlist the kings of England and Norway in a crusade against the Hohenstaufens. Rome itself became too Ghibelline for the Pope, who withdrew to Viterbo, where he died in 1261. He was buried in Viterbo Cathedral, but his tomb was destroyed during sixteenth-century renovations.