The incredible growth in Remote Sensing (RS) data volume, with high spectral-spatial-temporal resolutions, has been utilized in various application domains. With the rapid advancements in modern sensor technologies, including the 3D acquisition sensors, RS data with a large variety, velocity, veracity, varied value and incredible volume are generated, leading to the Remote Sensing Big Data (RSBD). With the high availability of RSBD, we require High-Performance Computing (HPC) environments for storing and processing these High-Dimensional (HD), complex, heterogeneous and distributed data. Also, introducing Deep Learning (DL) techniques in the RS domain demands more computing power, higher memory and networking bandwidth throughput capabilities, and optimized software and libraries to deliver the required performance. Motivated by this, we explore HPC computing environments for handling RSBD across multiple application domains in this paper. With particular emphasis on architectures such as cloud-based HPC, clusters, heterogeneous networks of computers, and specialized hardware architectures like Field Programmable Gate Arrays (FPGAs) and Graphics Processing Units (GPUs), we investigate how HPC technologies are being used to process RSBD efficiently while including integrated intelligence. This critical analysis results in a multi-layered cloud-based framework for efficient RSBD processing tasks. Also, we identified several data challenges to be handled while designing HPC frameworks. The findings from the study can help researchers better understand the HPC design concepts for developing RSBD frameworks.