•A review of literature studies on extractive distillation is provided.•Both continuous and batch extractive distillation processes are considered.•Separation of azeotropic mixtures and low relative volatility mixtures are shown.•The choice of the entrainer is discussed along with the process feasibility.•Process operation and control are surveyed. Extractive distillation processes enable the separation of non-ideal mixtures, including minimum or maximum boiling azeotropes and low relative volatility mixtures. Unlike azeotropic distillation, the entrainer fed at another location than the main mixture induces an extractive section within the column. A general feasibility criterion shows that intermediate and light entrainers and heterogeneous entrainers are suitable along common heavy entrainers. Entrainer selection rules rely upon selectivity ratios and residue curve map (rcm) topology including univolatility curves. For each type of entrainer, we define extractive separation classes that summarize feasibility regions, achievable products and entrainer – feed flow rate ratio limits. Case studies are listed as Supplementary materials. Depending on the separation class, a direct or an indirect split column configuration will allow to obtain a distillate product or a bottom product, which is usually a saddle point of rcm. Batch and continuous process operations differ mainly by the feasible ranges for the entrainer – feed flow rate ratio and reflux ratio. The batch process is feasible under total reflux and can orient the still path by changing the reflux policy. Optimisation of the extractive process must systematically consider the extractive column along with the entrainer regeneration column that requires energy and may limit the product purity in the extractive column through recycle. For the sake of reducing the energy cost and the total cost, pressure change can be beneficial as it affects volatility, or new process structures can be devised, namely heat integrated extractive distillation, extractive divided wall column or processes with preconcentrator.