 Hyperspectral remote sensing is based on measuring the scattered and reflected electromagnetic signals from the Earth's surface emitted by the Sun. These signals are often degraded by atmospheric effects and instrumental sensor noises such as Johnson noise, quantization noise, and shot noise. To reduce these noises, various noise reduction techniques have been proposed in the past decade, including band-wise and three-dimensional low-rank methods. Despite the advancements made in hyperspectral image processing, there remains a lack of a comprehensive overview of these techniques and their impact on hyperspectral imagery applications. This paper provides an overview of the techniques developed in the past decade for hyperspectral image noise reduction, as well as a discussion of the performance of these techniques when used as a pre-processing step for improving a hyperspectral image analysis task, classification. Additionally, this paper discusses the challenges associated with hyperspectral image modeling and denoising. Finally, it is shown that low-rank denoising techniques outperform other denoising techniques in terms of signal-to-noise ratio and spectral angle distance. This article was authored by Bennett Rasty, Paul Strunders, Pedram Gammasai, and others. We are article.tv, links in the description below.