Titanium alloys, due to their distinctive properties, are widely used in modern commercial applications. However, these alloys face challenges of machining via traditional techniques such as milling and turning. One of the unique thermal machining techniques that offer an effective choice with the highest dimensional precision and surface finish for Ti alloys is Wire Electrical Discharge Machining (WEDM). This method is based on the effect of erosion, where a highly repetitive electrical spark causes the material to be removed. The key challenges in WEDM are machining mode, wire electrode, dielectric, metal removal rate, and surface integrity as related to WEDM parameters were analyzed and correlated. Furthermore, Low metal removable rates, excessive tool wear, the production of recast layers, and heat-affected zones provide additional dilemmas when applied to titanium alloys. The majority of these obstacles occur as a result of titanium alloys' remarkable properties, such as low thermal conductivity, high melting temperature, and wear resistance. The first part of this paper highlights the research trends in WEDM on finding the relationships among various process parameters, such as cutting speed, the time between two pulses, servo voltage, peak current, dielectric fluid, wire tension, and machining modes that have a crucial impact on a variety of process responses, such as MRR, Ra, sparking gap, and WWR as well as surface integrity. The second part of the article also discusses various modeling, simulation, and optimization technique for monitoring process parameters to investigate the feasibility of various control practices for achieving the optimum machining conditions. The final part of the paper highlights these advancements and includes a roadmap for the potential future directions of WEDM research.