Multi-energy systems (MESs) use more than one energy vector to fulfil users' electrical, thermal, and cooling demands. This paper examines the recent developments in the design, optimisation, and implementation of MESs, focusing on residential applications. Firstly, recent advances in the design and optimisation of MESs are explained and analysed. The field is characterised by the proliferation of bespoke optimisation methods suitable for this kind of problem. Secondly, practical implementation in the laboratory of MESs and microgrids supplying electrical and thermal loads is discussed. The hardware requirements, in terms of controllers and converters, are critically analysed. This is contrasted with the real-world implementation of MESs or multi-output microgrids in the real world. A description of the communication infrastructure required for real-world implementation is discussed. Finally, a critical review of the entire process, the areas of challenge, and potential research opportunities are presented.