Robert Spencer, a very unPC expert on Islam, makes the point that Islam was not spread by the sword but that Islamic law was so spread.
A fine point, but one which illustrates the unique Muslim strategy for conversion of a territory which they control. Certainly the conquered peoples --as long as they are monotheists-- are "invited" to Islam. But, in principle, no one is forced to become Muslim.
The process is one of gradual attrition. "Muslim privilege" is enshrined in Muslim law and so is non-Muslim restriction, the sacred mandate of second-class citizenship --Muslim "Jim Crow", if you will. The easy way out is, of course, to convert.
Which is what happened, by and large.
Conquest by the sword creates the Muslim state and the imposition of Muslim law, sharia. Over time, the burden of sharia is what spreads Islam.