Titanium alloys are difficult to machine using conventional methods, therefore, nonconventional processes are often chosen in many applications. Electrical discharge machining (EDM) is one of those nonconventional processes that is used frequently for shaping titanium alloys with their respective pros and cons. However, a good understanding of this process is very difficult to achieve as research results are not properly connected and presented. Therefore, this study investigates different types of EDM processes such as, wire EDM, die-sink EDM, EDM drill and hybrid EDM used to machine titanium alloys. Machining mechanism, tool electrode, dielectric, materials removal rate (MRR), and surface integrity of all these processes are critically analysed and correlated based on the evidence accessible in literature. Machining process suffer from lower material removal rate and high tool wear while applied on titanium alloys. Formation of recast layer, heat affected zone and tool wear is common in all types of EDM processes. Additional challenge in wire EDM of titanium alloys is wire breakage under severe machining conditions. The formation of TiC and TiO2 are noticed in recast layer depending on the type of dielectrics. Removal of debris from small holes during EDM drilling is a challenge. All these restricts the applications EDMed titanium alloys in high-tech applications such as, aerospace and biomedical areas. Most of these challenges come up due to extraordinary properties such as, low thermal conductivity, high melting point and high hardness, of titanium alloys. Though hybrid EDM has been introduced and there is some work on simulation of EDM process, further developments in EDM of this alloy is required for widening the application of this methods.