Short answers, pulled from the story.
The Arab-Byzantine wars began in the late 620s following the death of Prophet Muhammad. The conflict started with the Battle of Mu'tah just months after Persian troops withdrew from Byzantine provinces in 629.
Emperor Constantine IV defeated the attacking Umayyad navy using Greek fire invented by Christian refugee Kallinikos of Heliopolis. The Muslim fleet suffered heavy losses from storms while the army lost many men to thematic armies on their route back.
The Plague of Justinian ravaged populations across both realms leaving them vulnerable to new threats before Arab forces emerged as a unified power under Islam. This vulnerability allowed Islamic expansion to open the door for prolonged conflict between Rome and Persia.
Muslim forces captured Damascus by 637 and Alexandria in September 642 extinguishing Byzantine rule in Egypt. They also completed the conquest of Cyrenaica between 643 and 644 while raiding Sicily in 652 and capturing Cyprus and Crete in 653.
The second massive siege occurred between July 717 and August 718 under Maslama ibn Abd al-Malik with 120,000 men and 1,800 ships. The besieging army suffered horrendous casualties from cold and lack of provisions before abandoning the siege on the 15th of August 718 due to famine and epidemic.