The Empire reached its peak in the 16th century, under the reign of Suleiman the Magnificent, whose armies reached Vienna in 1529 and 1532, but besieged them in vain. But conversely, this advance will mark the limit of the expansion of the Empire in the West (as Aden will set the limit in the East).
The Empire creates a military fleet, tries to impose itself in the Mediterranean to the detriment of the Italian cities and succeeds in doing so for a while. The naval defeat of Lepanto in 1571, before the Spanish and Venetian fleets, put an end to its supremacy. Reorganized by Sokullu Mehmed Pasha, the Ottoman fleet will certainly remain an important power thereafter, and the Venetian possessions (Cyprus and the islands in the Aegean Sea) will gradually join the Empire, but trade in the Mediterranean will remain in the hands of Western Europeans.
The Empire finds its place in the European diplomatic game where it is a traditional ally of France, in a reverse alliance against the Habsburgs, from the reign of François Ier.