Carbon capture and utilization (CCU) is recognized by the European Union, along with carbon, capture and storage (CCS), as one of the main tools towards global warming mitigation. It has, thus, been extensively studied by various researchers around the world. The majority of the papers published so far focus on the individual stages of a CCU value chain (carbon capture, separation, purification, transportation, and transformation/utilization). However, a holistic approach, taking into account the matching and the interaction between these stages, is also necessary in order to optimize and develop technically and economically feasible CCU value chains. The objective of this contribution is to present the most important studies that are related to the individual stages of CCU and to perform a critical review of the major existing methods, algorithms and tools that focus on the simulation or optimization of CCU value chains. The key research gaps will be identified and examined in order to lay the foundation for the development of a methodology towards the holistic assessment of CCU value chains.