The “breathable” outer layer is typically made of polyethylene, a thermoplastic. Inside that you’ll find a blend of cellulose pulp (in most brands, wood pulp is bleached with chlorine) and absorbent polymers. You may also find Velcro or adhesive tabs, chemical “wetness indicators” that change colors to show when the diaper is wet, and scents or lotions.
Check out this website for more detail on how a disposable diaper is made.
Most diaper companies do not use recycled materials to make their diapers, so the wood pulp is derived from freshly-harvested trees. The polymers that keep disposables dry on the outside and absorbent on the inside are petroleum products, but in the future manufacturers could try making these layers out of recycled milk jugs. (I am not a chemical engineer, so someone correct me if this idea isn’t feasible.) Even Seventh Generation, who makes a chlorine-free disposable diaper, does not use any recycled materials for the poly-wraps on their diapers and training pants. Their website says they plan to “upgrade this to 50% recycled content” in 2008. We’re not sure if they accomplished this goal or not!