English for Specific Purposes is an obligatory subject for the first two levels at the Sudanese Universities. It is taught as a university requirement. Accordingly, the students obsess on how to pass the examination, not to achieve any development in the language field. Even the teachers concentrate on the content rather than the skills, which the students ought to gain. This paper addresses the issue of English for Specific Purposes (ESP). It defines ESP with brief glimpse of its history and it attempts to highlight the line of demarcation of ESP and AEP. Moreover, it will endeavor the objectives of core course of ESP at the tertiary level in Sudanese Universities. Furthermore, how we should mobilize all the efforts to overcome the difficulties to promote the students competency in English language in their very field of specialization. As technology has created change in all aspects of society, it is also changing our expectations of what students must learn in order to function effectively. We should exploit the modern technologies effectively to radically change from teacher-centered approach to student-centered approach in teaching ESP. Consequently, the availability of computer and its utilization in different fields of specialization will be very facilitative and motivating for at least the contemporary generation.