Waste-to-energy processes remain essential to ensure the safe and irreversible removal of materials and substances that are (or have become) unsuitable for reuse or recycling, and hence, to keep intended cycles of materials in the circular economy clean. In this paper, the behavior of inorganic compounds in waste-to-energy combustion processes are discussed from a multi-disciplinary perspective, against a background of ever tightening emission limits and targets of increasing energy efficiency and materials recovery. This leads to the observation that, due to the typical complexity of thermally treated waste, the intelligence of combustion control systems used in state-of-the-art waste-to-energy plants needs to be expanded to better control the behavior of inorganic compounds that typically end up in waste furnaces. This paper further explains how this goal can be achieved by developing (experimentally validated) predictive numerical models that are engineering-based and/or data-driven. Additionally, the significant economic potential of advanced thermochemical intelligence towards inorganic compounds in waste-to-energy combustion control systems is estimated on the basis of typical operational figures.