Thermal Energy Storage Materials (TESMs) may be the missing link to the "carbon neutral future " of our dreams. TESMs already cater to many renewable heating, cooling and thermal management applications. However, many challenges remain in finding optimal TESMs for specific requirements. Here, we combine literature, a bibliometric analysis and our experiences to elaborate on the true potential of TESMs. This starts with the evolution, fundamentals, and categorization of TESMs: phase change materials (PCMs), thermochemical heat storage materials (TCMs) and sensible thermal energy storage materials (STESMs). PCMs are the most researched, followed by STESMs and TCMs. China, the European Union (EU), the USA, India and the UK lead TESM publications globally, with Spain, France, Germany, Italy and Sweden leading in the EU. Dissemination and communication gaps on TESMs appear to hinder their deployment. Salt hydrates, alkanes, fatty acids, polyols, and esters lead amongst PCMs. Salt hydrates, hydroxides, hydrides, carbonates, ammines and composites dominate TCMs. Besides water, ceramics, rocks and molten salts lead as STESMs for large-scale applications. We discuss TESMs' trends, gaps and barriers for commercialization, plus missing links from laboratory-to-applications. In conclusion, we present research paths and tasks to make these remarkable materials fly on the market by unveiling their potential to realize a carbon neutral future.