"It takes a membrane to make sense out of disorder in biology. You have to be able to catch energy and hold it, storing precisely the needed amount and releasing it in measured shares". So wrote Lewis Thomas in The Lives of Cells. Domains and rafts are shown in the present Review to play an important role in this amazing behavior of lipid membranes. Topics touched upon include the experimental detection of domains, their composition, domain induction, properties of rafts (a special form of domain), and the relationship of rafts to human diseases. Lipids, polymers, and proteins can contribute to this type of micro- and nanostructuring within membranes, thus imposing a new structural hierarchy on top of the classical bilayer membrane. The purpose of this Review is to develop an appreciation for the multiple organizational levels in self-assembling systems.