The heat-integrated distillation column to be addressed in this paper is a special distillation column that involves internal heat integration between the whole rectifying and the whole stripping sections. An overview of the research on this process is presented in this work. It covers from the thermodynamic development and evaluations to the practical design and operation investigations for the process. Comparative studies against conventional distillation columns are introduced and the results obtained show distinctively the substantial advantages in energy efficiency of the process over its conventional counterparts. Some relevant issues of process design and operation are to be stressed and the results of the first of its kind bench-scale plant experimentation are given in great detail. The application of internal heat integration principle to other distillation-related processes is also discussed in depth. These include heat integration within batch distillation columns, pressure-swing distillation columns that are used for the separation of pressure-sensitive binary azeotropes, and different distillation columns that have no connections at all. The prospects of the HIDiC and our future research work are then highlighted.