Mitigation of fossil carbon dioxide emissions from the main industrial sectors is a key element in the fight against global warming and climate change. In this respect, the main fossil energy-intensive processes (e.g., heat and power generation, cement, iron and steel, chemical applications etc.) are to be decarbonized for the future low-carbon economy. This paper is evaluating the post-combustion carbon capture based on innovative Calcium Looping (CaL) technology to be applied for decarbonization of various fossil-based industrial applications e.g., power generation, cement, iron and steel production. As illustrative cases, relevant industrial size systems are considered (e.g., 1,000 MW power plants, 4 Mt/year steel mills, 1 Mt/year cement plants). As benchmarks, similar processes without carbon capture as well as ones using chemical gas-liquid absorption for carbon capture are considered to assess the energy penalty for decarbonization. The decarbonized systems have 90 % carbon capture rate. As assessment tools a wide range of process systems engineering elements are used as follow: mathematical modelling and simulation using ChemCAD software, model validation based on experimental data, thermal integration analysis using pinch method for optimization of overall energy efficiency, technical and environmental evaluation to quantify the key performance indicators. As the results show, the innovative calcium looping technology for post-combustion carbon capture has significant advantages in comparison to the chemical gas-liquid absorption in term of higher overall plant energy efficiency (by about 2 net energy efficiency percentage points), lower CO2 capture energy penalty (7 - 8 vs. 10 net energy efficiency percentage points), reduced specific CO2 emissions etc.