With the development of an energy sector based on renewable primary sources, structural changes are emerging for the entire national energy system. Initially, it was estimated that energy generation based on fossil fuels would decrease until its disappearance. However, the evolution of CO2 capture capacity leads to a possible coexistence for a certain period with the renewable energy sector. The paper develops this concept of the coexistence of the two systems, with the positioning of green hydrogen not only within the renewable energy sector but also as a transformation vector for carbon dioxide captured in the form of synthetic fuels, such as CH4 and CH3OH. The authors conducted pilot-scale research on CO2 capture with green H2, both for pure (captured) CO2 and for CO2 found in combustion gases. The positive results led to the respective recommendation. The research conducted by the authors meets the strict requirements of the current energy phase, with the authors considering that wind and solar energy alone are not sufficient to meet current energy demand. The paper also analyzes the economic aspects related to price differences for energy produced in the two sectors, as well as their interconnection. The technical aspect, as well as the economic aspect, of storage through various other solutions besides hydrogen has been highlighted. The development of the renewable energy sector and its demarcation from the fossil fuel energy sector, even with the transcendent vector represented by green hydrogen, leads to the deepening of dispersion aspects between the electricity sector and the thermal energy sector, a less commonly mentioned aspect in current works, but of great importance. The purpose of this paper is to highlight energy challenges during the current transition period towards climate neutrality, along with solutions proposed by the authors to be implemented in this phase. The current stage of combustion of the CH4−H2 mixture imposes requirements for the capture of the resulting CO2.