The study of molecular networks has been central to providing important insight into the nature of cellular mechanisms and their role in diseases and evolutionary processes. As well as assisting in biological advances, rigorous understanding of molecular networks is also needed when designing molecular-scale synthetic devices and nanorobots, for which a wide range of promising applications, from biosensors to smart therapeutics, have been envisaged. The inherent stochasticity of molecular networks necessitates probabilistic modelling, and to this end probabilistic verification techniques have been added to the repertoire of stochastic analysis methods, enabling the use of temporal logic to explore the network dynamics. This lecture will give an overview of how probabilistic modelling and verification techniques have been used to advance scientific discovery through predictive modelling carried out alongside experiments for molecular signalling pathways, and how this technology is being transferred to support the design processes at the nanoscale, including guiding assembly pathways of DNA origami, debugging of DNA logic circuits and ensuring reliability of computation with molecular walkers. Future research challenges in the field will also be discussed.