Titanium alloy has a high specific resistance, excellent machining performance is non-corrosive, and the capability to withstand greater temperatures while maintaining outstanding mechanical properties. This alloy is, therefore, the right choice for aerospace, maritime, biomedical, and industrial applications. But machinability of titanium alloy is challenging as a result of its poor thermal conductivity, highly chemically reactive, and low elastic modulus hence it is treated as a difficult-to-cut material. Fast tool wear is observed during the machining of titanium alloy in conventional machining methods. Therefore, unconventional processing methods are used for the treatment of titanium alloy. Electric discharge machining (EDM) is one of these unconventional machining processes which are used for cutting with high precision, having a high degree of machinability, and getting a better surface finish. It is considered the best choice for machining titanium alloy. In the EDM process, different techniques are used to understand the effects of process parameters such as polarity, peak current, electrode type, pulse on time, and gap voltage on material removal rate, tool wear rate, surface roughness, and wear ratio. This paper critically investigates different types of EDM processes, experimental setups used for machining of titanium alloy, the effect of different tool electrodes and dielectric media on machining parameters, machined surface characteristics, and metal removal rate and tool wear rate.