To me the idea of Empire is about diversity- but how did empires actually deal with diversity? I'm particularly interested in the Islamic Empires (Ottomans, Safavids, Mughals), China, and European maritime empires in the same area (the Portuguese, Dutch and British, for example). Any ideas of references or information would be great, or a sense of how somewhere changed it's policies over time? Or about anywhere else really... my knowledge of global history is sorely lacking.
The Ottomans used dozens of different tactics to control non-Muslim and non-Turkish land. These tactics varied over time and, even within a given timeframe, frequently varied by region. We're talking about everything from the sikayet (grievance administration) to millets (religious courts) to the Imperial Diwan (essentially a court of appeals) in Istanbul. For an issue this broad, you really need to start delving into books on Ottoman domestic issues. To give you an idea of just how huge a subject this is, Michael Ursinus published a book in '05 covering Rumelia province's sikayet system from 1781 until 1783. It's an entire book and it encompasses three years. In a single province. It's just case after case after case of legal disputes of all sorts. Some involve just Muslims, some Muslims and non-Muslims, some just involve non-Muslims. Some of them are amusingly menial (I think there's a case about a missing pig at one point), some deal with bigger issues like the murder of a member of one religious group by a member of another.
To drastically over-simplify, however: the Ottomans typically would elevate a local noble to head the territory and then settled Muslims and/or Turks in the region as timars (knights, basically). Sometimes this worked rather well. Sometimes it backfired spectacularly. A good example of this is the Ottoman conquest of the Mamluks. Everything was fine and dandy under Selim, but rebellions broke out immediately once he died. The first few years of Suleyman's reign were spent crushing rebellions in Syria and Egypt. Selim had a well-earned reputation for being ruthless; he handed out decapitations like they were candy. Suleyman was unproven and largely untested and aspiring warlords thought they could get one over on him. Once he taught his subjects the futility of revolt, the rebellions tapered off.
But it wasn't just rule by court and kilij. It was also rule by law. Suleyman is remembered in the West as the Magnificent; he's remembered in Turkey as the Law-Giver. The Ottomans valued the rule of law over almost anything else. The Ottomans generally didn't care what kind of god you worshiped or what language you spoke. As long as you kept the peace and paid your taxes, they didn't really care to intervene in your life. This doesn't really begin to change in any meaningful way until the 18th century or so.