The achievements occurred in nonlinear dynamics over the last 30 years entail a substantial change of perspective when dealing with vibration problems, since they are now deemed ready to meaningfully affect the analysis, control, and design of mechanical and structural systems. This paper aims at overviewing the matter, by highlighting and discussing the important, yet still overlooked, role that some relevant concepts and tools may play in engineering applications. Upon dwelling on such topical concepts as local and global dynamics, bifurcation and complexity, theoretical and practical stability, attractor robustness, basin erosion, and dynamical integrity, recent results obtained for a variety of systems and models of interest in applied mechanics and structural dynamics are overviewed in terms of analysis of nonlinear phenomena and their control. The global dynamics perspective permits to explain partial discrepancies between experimental and theoretical/numerical results based on merely local analyses and to implement effective dedicated control procedures. This is discussed for discrete systems and reduced order models of continuous systems, for applications ranging from macro- to micro/nanomechanics. Understanding of basic phenomena in nonlinear dynamics has now reached such a critical mass that it is time to exploit their potential to enhance the effectiveness and safety of systems in technological applications and to develop novel design criteria.