In this paper, we present the classification and review of security schemes in mobile computing system. We classify these schemes based on types the infrastructure used in the mobile computing system-Mobile Ad Hoc Networks (MANET) and Mobile Agent model. Mobile Ad Hoc Networks are pervasive, ubiquitous and without any centralized authority. These unique characteristics, combined with ever-increasing security threats, demand solutions in securing ad hoc networks prior to their deployment in commercial and military applications. This paper reviews the prevailing mobile ad hoc network security threats, the existing solution schemes, their limitations and open research issues. We also explain the Intrusion detection and response technique as an alternate method to protect the MANET based mobile computing systems and their approaches. A literature review of important existing Intrusion Detection approaches and Intrusion Response Approaches for MANET is also presented. This paper also presents the limitations of existing Intrusion Detection and Response Approaches for MANET and open research issues in providing MANET security. With respect to Mobile Agent based mobile computing system, we have presented the classification of various types of security attacks in Mobile Agent based model and presented the security solutions for those type of attacks proposed by the various schemes and the open research issues in providing security for Mobile Agent based mobile computing system. Such classification enhances the understanding of the proposed security schemes in the mobile computing system, assists in the development and enhancement of schemes in the future and helps in choosing an appropriate scheme while implementing a mobile computing system.