Advances in sensor and computer technology are revolutionizing the way remotely sensed data is collected, managed and analyzed. In particular, many current and future applications of remote sensing in Earth science, space science, and soon in exploration science will require real- or near real-time processing capabilities. In recent years, several efforts have been directed towards the incorporation of high-performance computing (HPC) models to remote sensing missions. A relevant example of a remote sensing application in which the use of HPC technologies (such as parallel and distributed computing) is becoming essential is hyperspectral remote sensing, in which an imaging spectrometer collects hundreds or even thousands of measurements (at multiple wavelength channels) for the same area on the surface of the Earth. In this paper, we review recent developments in the application of HPC techniques to hyperspectral imaging problems, with particular emphasis on commodity architectures such as clusters, heterogeneous networks of computers, and specialized hardware devices such as field programmable gate arrays (FPGAs) and commodity graphic processing units (GPUs). A quantitative comparison across these architectures is given by analyzing performance results of different parallel implementations of the same hyperspectral unmixing chain, delivering a snapshot of the state-of-the-art in this area and a thoughtful perspective on the potential and emerging challenges of applying HPC paradigms to hyperspectral remote sensing problems.