Distributed computing is a computing in which different components and objects comprising an application can be located on different computers connected to a network. For example, a word processing application might consist of an editor component on one computer, a spell-checker object on a second computer, and a thesaurus on a third computer. In some distributed computing systems, each of the three computers could even be running a different operating system. Cloud computing has become a new age technology that has got huge potentials in enterprises and markets. Clouds can make it possible to access applications and associated data from anywhere. Companies are able to rent resources from cloud for storage and other computational purposes so that their infrastructure cost can be reduced significantly. Further they can make use of company ‘swide access to applications, based on pay-as-you-go model. Hence there is no need for getting licenses for individual products. However one of the major pitfalls in cloud computing is related to optimizing the resources being allocated. Because of the uniqueness of the model, resource allocation is performed with the objective of minimizing the costs associated with it. The other challenges of resource allocation are meeting customer demands and application requirements. Here, various resource allocation strategies and their challenges are discussed in detail. It is believed that this thesis would benefit both cloud users and researchers in overcoming the challenges faced.