Security requirements will change time to time. It is always necessary to provide appropriate security services to any communication. Later 1970’s many such mechanism has come. One among that is public key cryptography. The invention of RSA algorithm brings one of the significant improvements in the field of cryptography. Until that period, only symmetric key cryptography was in act which used only one key for both encryption and decryption. This makes that single key as the most sensitive one. Because of that key will be disclosed then entire communication will be compromised irrespective of the complexity of conversion applied over it. That is the reason why when this idea was proposed; it opened another window in the security providing arena. Hence the researchers have shown lot of interest in developing similar algorithms which gain some momentum over a period of time. At the same time this new approach has also started facing various hurdles in the name of various attacks. In that way this approach had a long history of over 40 years. During this period of time many modified approaches also were proposed by slightly modifying this one. On the other side some other approaches like elliptic curve cryptography also proposed based on the idea of public key cryptography. The purpose of this paper is to analyze the present scenario of RSA algorithm along with its past history in the modern cryptography era. Also this paper presents various related work done over a period of time related to this algorithm along with the summary of all the works. © 2016, International Journal of Pharmacy and Technology. All rights reserved.