During the recent years, Information and Communication Technologies (ICT) play a significant role in the field of education and e-learning has become a very popular trend of the education technology. However, with the huge growth of the number of users, data and educational resources generated, e-learning systems have become more and more expansive in terms of hardware and software resources, and many educational institutions cannot afford such ICT investments. Due to its tremendous advantages, cloud computing technology rises swiftly as a natural platform to provide support to e-learning systems. This paper focuses on the research on the application of cloud computing in e-learning. The aim of this paper is to give an overview of the current state and the impact of the use of cloud computing for e-learning. Thus, at first the paper introduces concepts of e-learning and cloud computing infrastructure with their key characteristics. The paper analyzes also challenges facing e-learning systems deployment. In follow the paper considers cloud-based e-learning solutions by focusing on the raisons of the convenience of cloud computing for e-learning. Therefore cloud computing benefits are introduced as a solution for these challenges. Finally, the paper presents some solutions of cloud computing in e-learning and describes the most common architecture adopted. Issues in implementing cloud-based e-learning systems and some potential ways to overcome them are also discussed.