Big Earth data are produced from satellite observations, Internet-of-Things, model simulations, and other sources. The data embed unprecedented insights and spatiotemporal stamps of relevant Earth phenomena for improving our understanding, responding, and addressing challenges of Earth sciences and applications. In the past years, new technologies (such as cloud computing, big data and artificial intelligence) have gained momentum in addressing the challenges of using big Earth data for scientific studies and geospatial applications historically intractable. This paper reviews the big Earth data analytics from several aspects to capture the latest advancements in this fast-growing domain. We first introduce the concepts of big Earth data. The architecture, various functionalities, and supporting modules are then reviewed from a generic methodology aspect. Analytical methods supporting the functionalities are surveyed and analyzed in the context of different tools. The driven questions are exemplified through cutting-edge Earth science researches and applications. A list of challenges and opportunities are proposed for different stakeholders to collaboratively advance big Earth data analytics in the near future.