With the increased share of renewable energy sources, there is a growing need for more flexibility to ensure the efficient and reliable operation of the electricity system. Multi-energy systems (MES) now appear as one possible means to provide such flexibility through increased synergies between electricity, gas, and heating/cooling systems. In this context, the main findings of the study carried out in the MAGNITUDE European project are described. The most relevant services that could be provided by MES to the electricity system are first presented. Then a methodology is proposed to characterise and compare the market organisations and mechanisms for their procurement. The results of its application in seven case study countries are summarised and illustrate the diversity met between countries. The gas and heat sectors are also investigated for the seven countries to characterise the main aspects relevant to the provision of the services by MES. A comparative analysis is then carried out between the three energy sectors in the seven countries and highlights the major similarities and differences. Finally, potential barriers for the provision of the services by MES are discussed regarding the market, regulatory, and cultural aspects.