Cloud Computing refers to providing computing and communications-related services with the aid of remotely located, network-based resources without a user of such resources having to own these resources. The network in question typically, though not necessarily, is the Internet. The resources provisioned encompass a range of services including data, software, storage, security, and so on. For example, when we use a mail service such as Gmail, watch a movie on YouTube, shop at Amazon.com, or store files using DropBox, we are using cloud-based resources (The Google Chrome Team, 2010). In this chapter, the authors examine the evolution of Cloud Computing from its early roots in mainframe-based computing to the present day and also explain the different services rendered by Cloud Computing in today’s business and personal computing contexts. This chapter provides a comprehensive view of the rapidly flourishing field of Cloud Computing and sets the stage for more in-depth discussions on its security, trust, and regulatory aspects elsewhere in this compendium.