Electrical discharge machining (EDM) is one of the most widely used non-conventional methods to machine electrically conductive materials in the manufacturing industry because of its strong capability in machining difficult-to-cut materials irrespective of their strength and hardness. Electrical discharge drilling (EDD) is an important variant of EDM. Due to the limitation of conventional drilling processes, special holes, particular those with high aspect ratios on hard-to-cut materials, can only be drilled by EDD. Extensive research has been carried out to improve the efficiency and quality of the EDD process by using different approaches, such as assisted EDD and powder-mixed EDM drilling aiming to improve the material removal rate (MRR), tool wear rate (TWR), surface quality and accuracy. This paper provides a comprehensive review of the EDD process. Different methods were compared; the advantages and disadvantages of each process were summarised; state-of-the-art technologies and the latest development were introduced, and research trends and new directions were presented.