Living systems are typical examples of dynamical systems with many interrelated parts or subsystems, from small-scale cellular relationships to large-scale population relationships. Nonlinear dynamics arise when the behaviour of one subsystem, with its own dynamics, becomes the input for another subsystem, imposing certain constraints on its dynamics. Mathematics, physics, and biological sciences have contributed important theoretical developments to the understanding of how nonlinear dynamics explain behaviour in a wide range of disciplines in natural sciences, social sciences, and life sciences, based on common principles arising from differential equations. Nonlinear dynamics underlie the developmental trajectory of living organisms; the spread of information in neural networks and disease in populations; and the prediction of evolving ecosystems in changing environments. While different challenges arise in each research area, the required quantitative models are shared across areas. These models, accompanied by statistical and computational tools, provide young scientists with a platform to understand the dynamics of their systems and to guide new experiments. As a result, the fields of mathematical and computational modeling have had significant impact across the natural and life sciences, including neuroscience, physiology, immunology, computer science, ecology, and evolutionary biology.