Application Service Providers (ASPs) are increasingly adopting the cloud computing paradigm to provision remotely available resources for their applications. In this context, the ability of cloud computing to provision resources on-demand in an elastic manner is of the utmost practical interest for them. As a consequence, the field of cloud computing has witnessed the development of a large amount of elasticity management solutions deeply rooted in works from distributed systems and grid computing research communities. This chapter presents some solutions that differ in their goals, in the actions they are able to perform and in their architectures. In this chapter, we provide an overview of the concept of cloud elasticity and propose a classification of the mechanisms and techniques employed to manage elasticity. We also use this classification as a common ground to study and compare elasticity management solutions.