Can you specify a time period in particular? The immediate consequences of Islam's expansion was war and conquest from 630-720. Regardless, in 686-7 a treaty was created wherein the Arabs, due to a civil war, paid the empire a thousand dinars weekly and a tribute of horses not to attack. Similarly, at the height of the crusading period, Isaak II Angelos was in alliance or at least non-conflict pact with Saladin to the detriment of the Third Crusade.

Islam and the various Caliphates were never monolithic. Until c.1180 the Byzantines maintained various centres of co-existence in Asia Minor alongside the Turks which the Latins found incomprehensible when they passed thru the land on pilgrimage.

There were times of great conflict certainly but also times of peace.

If you have a specific period in mind please state it and we can go into much greater depth. It is difficult to summarise 800 years.