This book constitutes the refereed proceedings of the 4th International Conference on Unconventional Computation, UC 2005, held in Sevilla, Spain in September 2005. The conference formerly was named Unconventional Models of Computation (UMC). The 19 revised full papers presented together with 5 invited full papers were carefully reviewed and selected for inclusion in the book. All major areas of unconventional computing models are covered in theory as well as in experiments and applications. Topics addressed are: natural computing including quantum, cellular, molecular, neural and evolutionary computing; chaos and dynamical systems based computing; and various proposals for computations that go beyond the Turing model.