Theodicy--Rod Dreher wonders about the doctrine

Thinking about the farmer's essay and what Pakistanis are going through got me to wondering about the tradition of theodicy in Islam. Theodicy is the term used to mean theological explanations for the existence of evil. Here is a marvelous interview with the Christian theologian David Bentley Hart, in which he discussed theodicy in the Christian tradition. I don't know how the existence of evil is generally explained by Islamic theologians, and would appreciate any guidance from readers. You may be familiar with the infamous Lisbon earthquake of 1755, and the resulting tsunami. The massive destruction and loss of life it caused had a major effect on European intellectual currents at the time, causing many to doubt God's providence, or God himself. It seems to me that this is a case of a horrific natural disaster occurring at a time when serious fault lines in religious belief were already opening across European culture; the earthquake and tsunami only exacerbated the rupture.