We report on the spontaneous emergence of computation from adaptive synchronization of networked dynamical systems. The fundamentals are nonlinear elements, interacting in a directed graph via a coupling that adapts itself to the synchronization level between two input signals. These units can emulate different Boolean logics, and perform any computational task in a Turing sense, each specific operation being associated with a given network's motif. The resilience of the computation against noise is proven, and the general applicability is demonstrated with regard to periodic and chaotic oscillators, and excitable systems mimicking neural dynamics.