This book covers the latest ideas and approaches in strongly nonlinear dynamical and acoustical systems and discusses appropriate modelling tools and practical examples highlighting the non-standard and non-stationary aspects of this challenging, yet so promising area. The contributions investigate and present the intentional use of nonlinearity in the most challenging field of acoustics, the latest developments in transient dynamics of strongly nonlinear systems, the subtle numeric problems arising while exploring nonlinear normal modes, the fascinating topic of nonlinear dynamics of wind musical instruments, the novel developments in the field of global nonlinear dynamics, some multi-faceted mathematical challenges in the dynamics of hysteretic systems, and lastly offers theoretical, numeric and experimental insights into the intricate dynamics of systems with contact nonlinearities. The need for such a work is underscored by the fact that accounting for, understanding of, and designing with nonlinearities is becoming an emerging universal trend in engineering practice, and is predicted to be even more so in the future. The book demonstrates that the idea of exploiting strong nonlinearity in dynamical and acoustical systems has transitioned from few early theoretical works to a diverse theoretical and experimental body of current research.