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Synthesis is the automated construction of a system from its specification. In the classical temporal synthesis algorithms, it is always assumed the system is “constructed from scratch” rather than “composed” from reusable components. This, of course, rarely happens in real life. In real life, almost every non-trivial commercial system, either in hardware or in software system, relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. In this work we de·ne and study the problem of LTL synthesis from libraries of reusable components. We de·ne two notions of composition: data-·ow com- position, for which we prove the problem is undecidable, and control-·ow com- position, for which we prove the problem is 2EXPTIME-complete. As a side bene·t we derive an explicit characterization of the information needed by the synthesizer on the underlying components. This characterization can be used as a specification formalism between component providers and integrators.