This book presents recent advances in nonlinearspeech processing beyond nonlinear techniques. It shows that it exploitsheuristic and psychological models of human interaction in order to succeed inthe implementations of socially believable VUIs and applications for humanhealth and psychological support. The book takes into account themultifunctional role of speech and what is "outside of the box" (see BjörnSchuller's foreword). To this aim, the book is organized in 6 sections, eachcollecting a small number of short chapters reporting advances "inside" and"outside" themes related to nonlinear speech research. The themes emphasizetheoretical and practical issues for modelling socially believable speechinterfaces, ranging from efforts to capture the nature of sound changes inlinguistic contexts and the timing nature of speech; labors to identify anddetect speech features that help in the diagnosis of psychological and neuronaldisease, attempts to improve the effectiveness and performance of Voice UserInterfaces, new front-end algorithms for the coding/decoding of effective andcomputationally efficient acoustic and linguistic speech representations, aswell as investigations capturing the social nature of speech in signalingpersonality traits, emotions and improving human machine interactions.