Nonlinear dynamics, ubiquitous in both physical and social sciences, leads to extreme events whose complexity engenders strong perturbations to eco-systems. Assessing and predicting earthquakes and floods, tornadoes and hurricanes, weather and climate, or modeling anomalous dissipation, mixing and bursty reconnection are performed using a variety of tools. Diagnostic and prognostic tools include stochastic equations, laboratory experiments, observations, numerical simulations and analysis, statistics and big data retrievals, as well as mathematical and phenomenological modeling. Fractals, and scaling laws in general, are one such tool which will be reviewed in depth, with applications to the interior of the Earth, hydrology, the ocean, the atmosphere and in heliophysics. These tools will continue to evolve: How? And where will we be going with them? What are the challenges? In the framework of AGU’s Centennial, this session will assess where we are and what are the perspectives for progress.