Being a muslim myself, I have wondered how the rise of the islam and muslim life was chronicled by the rest of the world.
During the time of the Prophet Muhammad emissaries were sent to the various leaders in the region. They had a campaign against a city under Byzantine control towards the end of his life and suddenly within one generation they were at the door of Byzantium.
I have heard the story that Khalid bin Walid or Ayyub Ansari for instance sent a message in reply to Byzantine letter that muslims love to eat human flesh. And another story during the time of Umar, the second Caliph where a city surrended believing the muslims were sharpening their teeth to eat them when they were using the miswak. But as these are from muslim sources, i would like to hear what has been recorded (and survived) about the muslims from non-muslims.
Robert Hoyland's Seeing Islam as Others Saw it covers this exhaustively, but so far I haven't finished it.
No one at the time realized that they were witnessing the birth of an Arab, Muslim empire. The typical view was that the "Saracens" were the instrument of God's wrath (exactly what provoked that wrath varied) and that the Jews were also to blame.