The Economist has a few articles including this one that is an excellent primer on Islamic finance.

The whys and wherefores of Islamic finance

THE modern history of Islamic finance is often dated to the 1970s, with the launch of Islamic banks in Saudi Arabia and the United Arab Emirates. But its roots stretch back 14 centuries. Islamic finance rests on the application of Islamic law, or sharia, whose primary sources are the Koran and the sayings of the Prophet Muhammad. Sharia emphasises justice and partnership. In the world of finance that translates into a ban on speculation (or gharar) and on the charging of interest (riba). The idea of a lender levying a straight interest charge, regardless of how the underlying assets fare in an uncertain world, offends against these principles—though some Muslims dispute this, arguing that the literature in sharia covering business practices is small and that terms such as “usury” and “speculation” are open to interpretation.