This is actually a pretty complex topic, perhaps a little over my head, but I found it too interesting to avoid delving in. I will try to be as accurate as possible, but understand that this is the result of my limited research and I encourage those interested to study further. I did use wikipedia for this because it spelled things out in a clear way, but there are other resources out there.
Mu'tazilah is an Islamic school of speculative theology that flourished primarily in Basra and Baghdad in the 8th-10th centuries. Although the school of thought itself declined sharply in popularity - it is only adopted today by a minority of Muslim intellectuals - many of its doctrines and methodologies were effectively cannibalized by other schools of thought which did survive.
Like many schools, it developed over centuries and had many different evolutions and interpretations, as well as multiple subgroups that held different political priorities. Caliph al-Ma'mun espoused certain beliefs shared by Mu'tazilah school (and several others) that the Quran is the created word of God. But he instituted the Mihna - an Inquisition - against religious opponents of that belief in an attempt to gain full control over the religious sphere as well as the secular. The Mu'tazilis were seen as instigators of this persecution campaign and lost popularity.
The Mu'tazilis held the truths of Islam as their starting point and primary reference, but also relied on logic, as well as various philosophies (early Islamic, Greek, and Hellenistic). Issues they sought to address: "whether the Qur'an was created or eternal, whether evil was created by God, the issue of predestination versus free will, whether God's attributes in the Qur'an were to be interpreted allegorically or literally, etc." (http://en.wikipedia.org/wiki/Mu'tazili)
The Nature of God, and the Importance of Reason AND Revelation:
Their view on Divine Unity is quite interesting. At its core, its the same as the majority of Muslims - there is no God but God. What is different is how they view God's attributes. According to Seyyed Hossein Nasr, in his book Islam, "where the Quran asserts that God is the Hearer and the Seer, the Mu'tazilites claimed that hearing and seeing in this case had nothing to do with what we understand by these Attributes; otherwise we would have an anthropomorphic image of God." Basically, if we take a literal view that God sees in the way that humans see (with actual eyes), we are limiting his definition to human terms and God is far beyond human limitations. Also, they deny that God's attributes are separate from God's essence. Some Mu'tazilis took a metaphorical interpretation of the Quran in this regard, others simply chose to affirm the Attributes while believing they were beyond our understanding, and others avoided judgement on this issue altogether.
Curiously, they believed all humans with full mental faculties - even those without access to scripture or revelation - are obligated to seek knowledge of God's existence and attributes. They also believed that humans were capable of being moral without revelation, at least on a basic level. In other words, God gave us the capacity to know right and wrong in general, and he gave us revelations to elaborate on the details from that point. Thus, reason and revelation are complimentary, not contradictory.
This was just a brief look at the Mu'tazilah school of thought, and there is a lot more to study and say about it. I bring it up simply because I find some of their views compelling, although some others (which I didn't get into here) I don't really agree with. Still, it gives me hope that there are so many ideas out there, and maybe one day the propagation of ideas won't be equated with blasphemy, but rather as a noble quest for better understanding of the divine.
