RNA is a remarkably versatile molecule that has been engineered for applications in therapeutics, diagnostics, and in vivo information-processing systems. However, the complex relationship between the sequence and structural properties of an RNA molecule and its ability to perform specific functions often necessitates extensive experimental screening of candidate sequences. Here we present a generalized neural network architecture that utilizes the sequence and structure of RNA molecules (SANDSTORM) to inform functional predictions. We demonstrate that this approach achieves state-of-the-art performance across several distinct RNA prediction tasks, while learning interpretable abstractions of RNA secondary structure. We paired these predictive models with generative adversarial RNA design networks (GARDN), allowing the generative modelling of novel mRNA 5' untranslated regions and toehold switch riboregulators exhibiting a predetermined fitness. This approach enabled the design of novel toehold switches with a 43-fold increase in experimentally characterized dynamic range compared to those designed using classic thermodynamic algorithms. SANDSTORM and GARDN thus represent powerful new predictive and generative tools for the development of diagnostic and therapeutic RNA molecules with improved function.