The increasing performance gains in processing large volumes of data are associated with core integration into a single chip, known as systems-on-chip (SoCs). However, there is a pursuit of heterogeneous SoCs that harness the strengths of different processor and circuit technologies. Hardware accelerators are a solution used in heterogeneous SoCs to achieve high processing rates, low power consumption, real-time responsiveness, or reliability. Meeting these requirements is crucial in various domains, including space applications, remote sensing, and machine learning. In this context, hyperspectral image processing has a large data volume and requires an exhaustive processing computation time. This scenario is ideal for applying hardware accelerator, principally to classification through machine learning algorithms, like artificial neural networks. In this context, this chapter brings the fundamentals about hyperspectral image, machine learning algorithms, and hardware accelerators. We also present, as the main focus of this chapter, a survey of hardware accelerators based in artificial neural network algorithms applied in hyperspectral images. Also, in the survey, we present an analysis of fault tolerance techniques applied to machine learning algorithms with a focus in solutions in space systems.