Fifty years ago, Western experts thought Sufism would follow other antique social and religious forms into irrelevance and extinction, superseded by modernity. But Sufism is still going strong, not only in the Muslim world, but also in the West, where it is one of the major routes for conversion to Islam. Mark Sedgwick asks why Sufism has proved experts wrong, what role it plays today, and why so many find it attractive, both in the Muslim world and in the West.