Computer security is a complex undertaking within the traditional client-server architecture. As services and data are moved to the Cloud, security requirements change and become even more complex. Existing client-server security practices can be extended to address challenges specific to the Cloud environment. In this chapter, a contrast is made between traditional client-server environment with a Cloud environment - in terms of security challenges and solutions. In addition to enumerating and contrasting traditional challenges and solutions, the authors describe security challenges and solutions particular to the Cloud computing environment. The chapter describes, in terms of the pillars of security, key issues that should be addressed by an organization as it migrates to Cloud environments and propose solutions to these issues.