A reason for the longevity of the Byzantine Empire is how they managed their foreign relations. Armed combat was the primary method with the evolved traditions of the Roman Empire, however Byzantine diplomacy which eventuated with their many treaties was used extensively as well. A lot of what we know of the world (and Europe in particular) during the Middle Ages comes from the records of Byzantine scholars, which were detailing the Empire's interactions.
Byzantine and Persian-Turk relations
Göktürk relations: 6th–7th centuries
The Göktürks of the First Turkic Khaganate, which came to prominence in 552 CE, were the first Turkic state to use the name Türk politically. They played a major role with the Byzantine Empire's relationship with the Persian Sasanian Empire. The first contact is believed to be 563 and relates to the incident in 558 where the slaves of the Turks (the Pannonian Avars) ran away during their war with the Hephthalites.
The second contact occurred when Maniah, a Sogdian diplomat, convinced Istämi (known as Silziboulos in Greek writings) of the Göktürks to send an embassy directly to the Byzantine Empire's capital Constantinople, which arrived in 568 and offered silk as a gift to emperor Justin II. While the Sogdians were only interested in trade, the Turks in the embassy proposed an alliance against the Persians which Justin agreed to. The Persians had previously broken their alliance with the Turks due to the competitive threat they represented. This alliance guaranteed the arrival of west-bound silks from China and increased the risk of a war on two fronts for the Persians, with hostilities that would eventuate with the Byzantine–Sasanian War of 572–591. In 569 an embassy led by Zemarchus occurred which was well received and likely solidified their alliance for war.
Another set of embassies occurred in 575–576 led by Valentine which were received with hostility by Turxanthos due to alleged treachery. They required the members of the Byzantine delegation at the funeral of Istämi to lacerate their faces to humiliate them. The subsequent hostility shown by the new ruler Tardu would be matched in Byzantine writings. With the insults reflecting a breakdown of the alliance, the likely cause is that the anger was due to the Turks not having their expectations met from their agreements and realising they were being used when they no longer aligned with the current goals of the Byzantine Empire (who correspondingly lacked trust in the Turks as partners).
Years later, they would collaborate again when their interest aligned. The Turks attacked the Avars when they sacked a Byzantine city in the Balkans (Anchialos in 584). Toward the end of the Byzantine–Sasanian War of 602–628, the Turks allied with the Byzantine Empire and played a decisive role with the Third Perso-Turkic War.
Sasanian Persian relations: 3rd–7th centuries
The Sasanian Empire succeeded the Parthian Empire, the traditional arch-rival of the Roman Empire. They were recognized as one of the leading world powers alongside its main rival the Byzantine Empire. This was from the overthrow of the Parthian dynasty in the 3rd century by Ardashir I until their total collapse against the Arabs. There would be many wars between the rivals during this period.
The Byzantine Empire's final war weakened the Sasanian Empire which set up its destruction by the Arabs. The climactic Byzantine–Sasanian War of 602–628, which included the siege of the Byzantine capital Constantinople, ended with both sides having drastically exhausted their human and material resources. In 627, allied with Turks, Heraclius invaded the heartland of Persia. A civil war broke out in Persia, during which the Persians killed their king, and sued for peace. By the end of the conflict, both sides had exhausted their human and material resources and achieved very little. Consequently, they were vulnerable to the sudden emergence of the Islamic Rashidun Caliphate, whose forces invaded both empires only a few years after the war. The Muslim armies swiftly conquered the entire Sasanian Empire as well as the Byzantine territories in the Levant, the Caucasus, Egypt, and North Africa.
Seljuk relations: 11th–13th centuries
The Seljuk Turks was a Sunni Muslim dynasty from the Qiniq branch of the Oghuz Turks. They gradually became Persianate and contributed to the Turco-Persian tradition in the medieval Middle East and Central Asia. The Seljuks established both the Seljuk Empire and the Sultanate of Rum, which at their heights stretched from modern day Iran to Anatolia, and were targets of the First Crusade.