Language for specific purposes reveals some specificities quite complex to grasp and make use of, if not an explicit knowledge and an appropriate approach to the situation at hand is devoted to its teaching. This is why, it has been the study that goes back to the time of the ancient Greeks and Romans, and from its earliest days has caught the interest of the learned and the wise. Strevens (1977) says that the history of LSP teaching can go back to the 16th and 17th centuries. In fact, this was the period of new discoveries and experiments of new approaches to science which called for a language suitable for expressing accurately the new phenomena. The main concern of the present research work is to give a clear picture of the ESP teaching and learning situation in Algeria. First, this study draws a quick sketch on the Algerian ESP project background, then, restates the major objectives of ESP teaching. Besides, it presents the Algerian ESP teaching situation, the difficulties and barriers that English teachers encounter when dealing with this area of English as well as the need for change which will allow the learners to use the foreign language in their specific fields. A case in point is the teaching/learning of ESP to 1st year psychology students at Tlemcen University. The problem is that Algerian university students, and especially those of the 1st year, who have received at least seven years of formal English teaching in the middle and secondary schools still find themselves unable to use the English language, let alone make an effective use of it for specific purposes.