There is a fundamental relationship between belief propagation (BP) and maximum a posteriori (MAP) decoding which is reminiscent of Maxwell's construction in thermodynamics. BP and MAP decoding are connected to a common object which is the (G)EXIT function. The (general) area theorem is the central element in this theory. As a main application of the area theorem it can be shown that a Maxwell-type construction determines the MAP threshold from the BP (G)EXIT curve. But there are many other potential applications of (G)EXIT curves. (G)EXIT analysis turns out to be an efficient machinery which for example enables to extend to general channels the matching condition already known for the erasure channel. This condition asserts that transmission above capacity is not possible, using only quantities which naturally appear on the context of iterative coding.

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