Final answer:
The Islamic empire historically extended to what is now Pakistan in the east and the Iberian Peninsula (Spain and Portugal) in the west, during its peak.
Step-by-step explanation:
The eastern and western boundaries of the historical Islamic empire extended to present-day countries that were once under its control. The eastern boundary of the Islamic empire during its peak reached into what is today known as Pakistan, influenced by clashes with the rulers of Sindh and expansion into the region by the Muslim Umayyad state in the early 8th century. On the western front, the Islamic empire's reach spanned to the Iberian Peninsula, which encompasses modern-day Spain and Portugal, marking an era of remarkable diversity and cultural exchange during the Islamic rule there, termed the Islamic West. As history unfolded, the empire faced challenges and contraction, but these regions reflect the vast geographical expanse of Islamic influence at the time.