The death of Muhammad in 632 made confusion in the Muslim community. Muhammad had left no information on who should rule after him. After a long discussion by the members of the community, Abu Bakr was selected as the first Khalifah. The confusion did not end with Abu Bakr's succession. Tribes all around Arabia revolted. They still accepted Muhammad as a prophet but they refused to send taxes to Medina. Known as the "Riddah Wars", the revolts lasted until the end of 633. Even with these problems, Abu Bakr followed what Muhammad was going to do before he died and sent Muslim forces into Syria and Iraq. Before Abu Bakr died, he selected Umar Ibn al-Khattab as his successor.
The second khalifah Umar continued to send out troops, holding back the power of the Bedouin tribes. In 636 the Muslims defeated the Persians at Qadisiyya. After the battle, the Persians kept on retreating.
Then the Muslims conquered northern Iraq and moved into western Iran. After the battle at Nihavand in 642, the Persians couldn't handle any more fighting and the rest of Iran was open for defeat. The last king went to Khurasan and was killed in 651.
Meanwhile Umar continued the nasty war against the Byzantines in Syria. The Muslims reached Damascus in 635 but were forced to leave to Yarmuk, there they defeated the Byzantines with faith and then faced little battle in getting the rest of Syria and Palestine. The troops then marched into northern Iraq and Armenia, and into Egypt. The Byzantines gave up Egypt to the Muslims under a peace treaty in 641.
Umar allowed the conquered people to keep their land and religion they were given the name of "protected people" and were required to pay a special tax, known as the jizya.