In this day and age, it is absolutely indispensable for acquiring competence in English to grapple with the real impediments and huge challenges of the modern epoch. The emergence of English as a global language is among the factors that could explicate its vitality and its expansion. The basic burden of making language courses more relevant to learners' needs resulted in the advent of languages for specific purposes movement, known in English Language Teaching circles as English for Specific Purposes. ESP then, has since its inception in the early 1960s become one of the most dynamic branches of applied linguistics in general, and of Teaching English as a Foreign Language in particular. To amass relevant data, a case study was conducted through a combination of a questionnaire, classroom observation, and informal interviews with language teachers and subject specialists. The main aim of this present paper is to precisely delineate the teaching/learning process of ESP in the department of Computer Sciences at the University of ORAN1 in Algeria, and the learners' attitudes towards this teaching. For this purpose, it is necessary to explore the utility of ESP as perceived by learners, and to address problems faced by instructors. The results indicate that the students have a positive attitude towards ESP and that their poor achievement was due to multiple reasons. This digest concludes by offering some suggestions and implications as remedial actions to the major confronted concerns.