Chemical concepts such as structure, bonding, reactivity, etc. have been widely used in the literature and text books to appreciate molecular properties and chemical transformations. Even though modern theoretical and computational chemistry is well established from the perspective of accuracy and complexity, how to quantify these concepts is a still unresolved task. Conceptual density functional theory and its related recent developments provide unique opportunities to tackle this problem. In this Special Issue, 27 contributions from top investigators over the world are collected to highlight the state-of-art research on this topic, which not only showcases the status of where we are now but also unveils a number to possible future directions to be pursued.