Remote sensing data have become very widespread in recent years, and the exploitation of this technology has gone from developments mainly conducted by government intelligence agencies to those carried out by general users and companies. There is a great deal more to remote sensing data than meets the eye, and extracting that information turns out to be a major computational challenge. For this purpose, high performance computing (HPC) infrastructure such as clusters, distributed networks or specialized hardware devices provide important architectural developments to accelerate the computations related with information extraction in remote sensing. In this paper, we review recent advances in HPC applied to remote sensing problems; in particular, the HPC-based paradigms included in this review comprise multiprocessor systems, large-scale and heterogeneous networks of computers, grid and cloud computing environments, and hardware systems such as field programmable gate arrays (FPGAs) and graphics processing units (GPUs). Combined, these parts deliver a snapshot of the state-of-the-art and most recent developments in those areas, and offer a thoughtful perspective of the potential and emerging challenges of applying HPC paradigms to remote sensing problems.