This conference background note is developed for the Third Global Conference on Strengthening Synergies between the Paris Agreement and the 2030 Agenda for Sustainable Development. The note aims to address two questions: 1) What is known about synergies and trade-offs? and 2) What can be done to consolidate existing and emerging knowledge on these themes to raise ambitions and accelerate progress on climate change and the SDGs? The note shows significant evidence of synergies in urban systems but fragmented evidence elsewhere. It further underlines the potential to use co-benefits and water-food-energy nexus (WFEN) tools to shed light on interrelationships in specific contexts. It finally underlines the need for carefully crafted enabling environments to help translate evidence into actions.