Environmental processes such as, for instance, those affecting the distribution of water resources across the planet, the response of living organisms to environmental stimuli, carbon sequestration and storage in the lithosphere, etc. are key to the functioning of the Earth system and its components (Ecosphere). Such processes are characterized by deterministic (i.e. certain) and stochastic (i.e. uncertain) rules, which help govern ecosystem habitat formation, characteristics and species biodiversity. Compared to the pre-human era, the Ecosphere is now exposed to human actions that affect both biotic and abiotic processes across several spatial and temporal scales. As a result, many environmental processes are transgressing planetary boundaries previously considered safe for the Earth system to function properly. In this talk, we will examine how deterministic trends and random fluctuations affect water, energy and environmental processes and how their combination can lead to the resistance and resilience of ecosystems to perturbations. We shall examine pattern formation, plant growth and uprooting, and the effect of memory in water-driven systems as examples of the above processes, under both human-driven and climate change scenarios. In general, as far as environmental processes are concerned, we will learn that sustainable measures placed in defense of planetary boundaries must guarantee part of the original deterministic and noisy components of the process. The lecture will conclude with an overview of new perspectives for the transdisciplinary development of future environmental sciences and engineering.