After the Mongol invasions, there existed five main political centers in the Islamic world:
The first of there was the Ottomans who ruled over Turkey and much of Asia Minor. With their capture of Constantinople in 1413, the Ottomans became the most powerful of the Islamic empires.
In the Indian Subcontinent, a succession of Turkish Muslim dysnasties ruled over most of northern India. In the 16th century, the Mughal Empire was established by Babur, a descendent of Tamerlane from Central Asia in what is now Uzbekistan. The Mughul Empire ruled over South Asia till its final overthrow by the British in the late 1700s.
The Mamluk Sultanate of Egypt, Palestine and Syria survived the Mongol invasion and served for a while as the last stronghold of Arabic Islamic culture. In 1516-1517, it was incorporated into the Ottoman Empire.
In the 17th century, the Safavids founded a new monarchy in Iran. The Safavids were Shi’ites, which is still the main form of Islam practiced in Iran today.
The last major center of Islamic power in this period existed in the Eurasian steppes, in what is now southern Russia and Central Asia. The Khanate of the Golden Horde in Southern Russia and the Chaghatay Khanate in Central Asia consisted of two large states of Islamicized Mongols. Both states were later incorporated into the Russian empire.
During this period, Islam also advanced and retreated in several areas. In Southwest Europe, the Moors were finally driven from Spain, Portugal and Sicily. Even North Africa was for a short while occupied by Spaniards and Portugese. In Eastern Europe, the Ottomans advanced as far west as Vienna but eventually relinquished most of its conquests. The Golden Horde even managed to extend its rule north to Moscow for a while. Muslims from Arabia and India made the greatest inroads for Islam in Southeast Asia. By the 16th century, most of the Malay lands had converted to Islam.