This article gives a survey of state-of-the-art methods for processing remotely sensed big data and thoroughly investigates existing parallel implementations on diverse popular high-performance computing platforms. The pros/cons of these approaches are discussed in terms of capability, scalability, reliability, and ease of use. Among existing distributed computing platforms, cloud computing is currently the most promising solution to efficient and scalable processing of remotely sensed big data due to its advanced capabilities for high-performance and service-oriented computing. We further provide an in-depth analysis of state-of-the-art cloud implementations that seek for exploiting the parallelism of distributed processing of remotely sensed big data. In particular, we study a series of scheduling algorithms (GSs) aimed at distributing the computation load across multiple cloud computing resources in an optimized manner. We conduct a thorough review of different GSs and reveal the significance of employing scheduling strategies to fully exploit parallelism during the remotely sensed big data processing flow. We present a case study on large-scale remote sensing datasets to evaluate the parallel and distributed approaches and algorithms. Evaluation results demonstrate the advanced capabilities of cloud computing in processing remotely sensed big data and the improvements in computational efficiency obtained by employing scheduling strategies.