English for Specific Purposes, known as acronym-"ESP", has been a distinct activity in the field of English Language Teaching (ELT) since 1960s. The flowering period of ESP has been identified due to many incidents like the second world war in 1945, the rapid expansion in scientific, the growth of science and technology, the increased use of English as the international language of science, technology and business, the increased economic power of certain oil-rich countries and increased numbers of international students studying in English Speaking countries. Needs analysis is the key essence of ESP. The paper reviews the history and development of ESP, the notion of needs analysis in ESP setting and some important components of ESP needs analysis. Finally the paper critically reviews the ESP needs analysis models. TSA (Target Situation Analysis), PSA (Present Situation Analysis), LSA (Learning Situation Analysis), MA (Means Analysis) and Language Audit are the salient features of needs analysis in any ESP context. In the field of ESP, there are a number of models of needs analysis such as Munby (1978), McDonough (1984), Hutchinson & Waters (1987), Robinson (1991), West (1994), Jordan (1997) and Dudley-Evans & St. John (1998). These theoretical models are similar to a certain extent that they aim at identifying the English language needs of the learners. The paper provides the readers with a solid review on some ESP needs assessment models.