Short answer
Mu'tah was fought in Jumada al-Ula 8 AH (629 CE) in what is now Jordan, between about 3,000 Muslims and a far larger Byzantine and Ghassanid army. The three appointed commanders, Zayd, Ja'far and Abdullah ibn Rawaha, were martyred, and Khalid ibn al-Walid led a safe withdrawal.
The Sunni account, from Bukhari and the seerah books, is that the Prophet ﷺ named three commanders in order, all three were martyred, and Khalid, whom he called a sword from the swords of Allah, took the flag and saved the army.
The four schools agree on this.
Explanation
The Prophet ﷺ had sent an envoy, al-Harith ibn Umayr, with a letter to the ruler of Busra. A Ghassanid chief allied to Byzantium killed him on the way, which was a grave breach. He sent an army of about 3,000 north to Mu'tah, near al-Karak in present-day Jordan. He appointed Zayd ibn Haritha as commander and said: if Zayd is killed, then Ja'far; if Ja'far is killed, then Abdullah ibn Rawaha.
The Muslims met an army many times larger. Zayd fought until he was killed. Ja'far ibn Abi Talib took the flag; he lost both hands and held it with his arms until he fell. Ibn Umar, who was in the army, counted more than ninety wounds on his body. Abdullah ibn Rawaha took it and was killed too. The Companions then chose Khalid ibn al-Walid, who had become Muslim only months before. He reorganised the lines and withdrew the army safely. Khalid said nine swords broke in his hand that day.
In Madinah, the Prophet ﷺ told the people of each death as it happened, with tears in his eyes, then said that a sword from the swords of Allah had taken the flag and Allah gave them victory. Ja'far became known as al-Tayyar (the flier), because he said Allah gave Ja'far two wings in Paradise in place of his hands.
Mu'tah was the first major clash with the Byzantine side and was followed a year later by the expedition of Tabuk. See Battle of Tabuk, Khalid ibn al-Walid and Seerah.
The evidence
Sahih al-Bukhari 4261
Sahih... إن قتل زيد فجعفر ...
"If Zayd is killed, then Ja'far."
He named the three commanders in order.
Sahih al-Bukhari 4262
Sahih... حتى أخذ الراية سيف من سيوف الله ...
"Until a sword from the swords of Allah took the flag."
Khalid's title and the safe outcome, told with tears.
Sahih al-Bukhari 4265
Sahih... لقد انقطعت في يدي يوم مؤتة تسعة أسياف ...
"Nine swords broke in my hand on the day of Mu'tah."
Khalid describes the fighting.
Where the ruling is recorded
- Sirat Ibn Hisham, Account of the expedition to Mu'tah. The killing of the envoy, the army and the three commanders.
- Zad al-Ma'ad (Ibn al-Qayyim), Section on the expedition to Mu'tah. Lessons of the battle and the Prophet's naming of commanders.
- Fath al-Bari (Ibn Hajar), Commentary on Kitab al-Maghazi, chapter on the expedition of Mu'tah in the land of Syria. Discusses whether the outcome was a victory or a withdrawal.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.