Cloud computing has recently evolved as a popular computing infrastructure for many applications. Scientific computing, which was mainly hosted in private clusters and grids, has started to migrate development and deployment to the public cloud environment. eScience as a service becomes an emerging and promising direction for science computing. We review recent efforts in developing and deploying scientific computing applications in the cloud. In particular, we introduce a taxonomy specifically designed for scientific computing in the cloud, and further review the taxonomy with four major kinds of science applications, including life sciences, physics sciences, social and humanities sciences, and climate and earth sciences. Our major finding is that, despite existing efforts in developing cloud-based eScience, eScience still has a long way to go to fully unlock the power of cloud computing paradigm. Therefore, we present the challenges and opportunities in the future development of cloud-based eScience services, and call for collaborations and innovations from both the scientific and computer system communities to address those challenges.