The question as put is unanswerable. There are over 25 different Caliphates that have fought innumerable battles. Please be more specific.
To derail Ali's caliphate
The Battle of Ascalon pitted the French Crusaders against the Egyptian Fatimid Caliphate.
The Muslim forces at the Battle of Tours were from the Caliphate of the Umayyad dynasty.
Hercules engaged in battle with the Hydra at the Lernaean Swamp.
The SASSANID EMPIRE was defeated at the Battle of Nahavand and all of their territories were annexed by the Rashidun Caliphate.
Abbasid Caliphate.
Rashidun Caliphate was created in 632.
Take Midway Island and engage US fleet in a decisive battle.
Abbasid caliphate -- Baghdad Ummayyad Caliphate- Cordoba
fight
Battle of Yarmuk had destroyed major power of Eastern Roman Empire's army in Syria. They couldn't rely on their Christian Arab anymore. Islamic Caliphate could easily capture Syria after this battle.
Caliphate of Córdoba ended in 1031.