Nonlinear Signal Processing is an emerging discipline combining knowledge from signal processing, adaptive systems, nonlinear dynamical systems, statistics and information theory, computation, and mixed-signal processing systems realization. Nonlinearity shows itself as a curse in many physical system realizations where analog effects may deviate strongly from their idealized linear behavior. The modeling of these nuisance effects and their adaptive digital compensation is a key application of nonlinear signal processing in the realm of mixed-signal processing systems such as power amplifiers for wire-line and wireless communications. Nonlinearity can also be a blessing when it comes to the modeling, compression, and interpretation of information sources where deterministic nonlinear dynamics rivals with conventional statistical models in representing randomness of a source, i.e., its innovation or information content. This gives rise to more accurate signal models and to an understanding of information flow in computational algorithms and distributed signal processing networks. This research area strongly interacts with the art of algorithm engineering as an extension to circuit and system design, including the mapping on reconfigurable architectures.