The widespread adoption of renewable energy sources has greatly contributed to the fight against climate change. This success, however, has put a significant strain on power grids. Further integration of renewable energy sources, while necessary, will require a smarter use of existing infrastructure. Power-to-gas, electric vehicles and heat pumps already allow us to provide flexibility by shifting energy use across domains. This thesis explores how new market designs can better facilitate such multi-energy flexibility. This work discusses both foundational questions of multi-dimensional energy trading and conceptual questions of applying fairness and honesty to multi-dimensional energy markets: What are fair unit-prices when energy can be shuffled across time? How can an agent be incentivized to be honest about its forecast when it does not know it perfectly itself?