The challenge of transitioning to a climate-neutral European economy requires coordinated action in various energy sectors, emphasizing the critical role of managing both carbon dioxide (CO2) and hydrogen (H2). Hydrogen infrastructure must effectively interact with carbon management technologies like capture, transport, storage, and sequestration. Hydrogen is seen as a viable option in industries not suitable for electrification due to its efficiency in energy transportation and storage. The production of carbonaceous fuels by combining carbon with hydrogen offers sustainability benefits. Various European programs and initiatives aim to boost the hydrogen and carbon economy, aligning with the EU's climate neutrality target by 2050. Initiatives like the European Hydrogen Backbone and the Northern Lights project in Norway highlight the potential of hydrogen and carbon management technologies. Techno-economic studies are crucial to understanding the intricate interplay between hydrogen and carbon networks for a comprehensive view of the energy system in Europe.