Big Data has emerged in the past few years as a new paradigm providing abundant data and opportunities to improve and/or enable research and decision-support applications with unprecedented value for digital earth applications including business, sciences and engineering. At the same time, Big Data presents challenges for digital earth to store, transport, process, mine and serve the data. Cloud computing provides fundamental support to address the challenges with shared computing resources including computing, storage, networking and analytical software; the application of these resources has fostered impressive Big Data advancements. This paper surveys the two frontiers-Big Data and cloud computingand reviews the advantages and consequences of utilizing cloud computing to tackling Big Data in the digital earth and relevant science domains. From the aspects of a general introduction, sources, challenges, technology status and research opportunities, the following observations are offered: (i) cloud computing and Big Data enable science discoveries and application developments; (ii) cloud computing provides major solutions for Big Data; (iii) Big Data, spatiotemporal thinking and various application domains drive the advancement of cloud computing and relevant technologies with new requirements; (iv) intrinsic spatiotemporal principles of Big Data and geospatial sciences provide the source for finding technical and theoretical solutions to optimize cloud computing and processing Big Data; (v) open availability of Big Data and processing capability pose social challenges of geospatial significance and (vi) a weave of innovations is transforming Big Data into geospatial research, engineering and business values. This review introduces future innovations and a research agenda for cloud computing supporting the transformation of the volume, velocity, variety and veracity into values of Big Data for local to global digital earth science and applications.