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. The authors review recent efforts in developing and deploying scientific computing applications in the cloud. In particular, they 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.