Excessive CO2 emissions in the atmosphere from anthropogenic activity can be divided into point sources and diffuse sources. The capture of CO2 from flue gases of large industrial installations and its conversion into fuels and chemicals with fast catalytic processes seems technically possible. Some emerging technologies are already being demonstrated on an industrial scale. Others are still being tested on a laboratory or pilot scale. These emerging chemical technologies can be implemented in a time window ranging from 5 to 20 years. The massive amounts of energy needed for capturing processes and the conversion of CO2 should come from low-carbon energy sources, such as tidal, geothermal, and nuclear energy, but also, mainly, from the sun. Synthetic methane gas that can be formed from CO2 and hydrogen gas is an attractive renewable energy carrier with an existing distribution system. Methanol offers advantages as a liquid fuel and is also a building block for the chemical industry. CO2 emissions from diffuse sources is a difficult problem to solve, particularly for CO2 emissions from road, water, and air transport, but steady progress in the development of technology for capturing CO2 from air is being made. It is impossible to ban carbon from the entire energy supply of mankind with the current technological knowledge, but a transition to a mixed carbon–hydrogen economy can reduce net CO2 emissions and ultimately lead to a CO2-neutral world.