What happened
Between 639 and 642, Arab Muslim forces led by the general Amr ibn al-As, under the caliph Umar, took Egypt from the Byzantine Empire. An initial force of a few thousand — the numbers in early accounts vary — was later reinforced; it won a victory at Heliopolis in 640 and took the fortress of Babylon, in what is now Old Cairo, in 641. Alexandria was handed over by treaty the same year, and a Byzantine attempt to retake it in 645 was repelled. The victors founded Fustat as the new capital in place of Alexandria.
Background
Byzantine Egypt was exhausted by the long war with Sasanian Persia, which had occupied the country from 619 to 629. It was also divided by Christian doctrinal strife between the imperial (Chalcedonian) church and the Egyptian Miaphysites.
Consequences
The conquest began the Islamic era of Egypt. Christians and Jews continued to practice their faiths as protected communities paying a poll tax under early Islamic law. Over the following centuries Arabic replaced Coptic and Greek in administration and daily life, and Egypt became a wealthy province of the caliphates and a springboard for further expansion.