To limit global temperature rise to below 2°C, we need to radically and rapidly change the way we build and use materials, since construction is responsible for 20‐40% of industrial CO2 emissions. Magnesium carbonate‐based cements have the potential to become a major carbon sink in construction industry, as CO2 will not be emitted during their production, but CO2 will rather be bound during hardening. Two different reaction mechanisms lead to setting and hardening of such HMC cements: i) hydration of MgO‐Mg‐carbonate, also in blends with silica and other mineral additions, in the presence of water or salt solutions (such as sodium bicarbonate solution) at ambient conditions or ii) carbonation hardening of MgO‐based systems at increased CO2 partial pressure and/or at increased temperatures.However, the utilization of hydrated magnesium carbonate and magnesium silicate cements is currently hampered by the lack of systematic experiments and of fundamental understanding of the factors affecting the hardening process, mechanical properties, long‐term behavior and durability. In particular, the role of temperature, relative humidity and addition of supplementary cementitious materials and/or industrial by‐products has not been systematically investigated. We need knowledge both on the practical side through systematic experiments with pastes, mortars and concretes as well as on a fundamental level through solubility and sorption experiments and thermodynamic modelling. In addition, reaction kinetics need to be optimized as well as the early formation of the preferred phases (stability enhancement) to develop efficient HMC cements for construction. Due to the socio‐economic relevance of cement and concrete, the impact of such “carbon”‐negative cements may go beyond a purely scientific one and lead to technological breakthroughs to the benefit of environment and society.