HSI is a robust technology that covers the spectral information in detailed manner over the wide range of wavelengths, makes it successful in the domain of medical imaging, agriculture and majorly in remote sensing. But sometimes hyperspectral images are targeted by noise due to environmental reasons, imperfections in sensors and data transmission errors. Effective denoising of images is must so that the quality of hyperspectral images can be maintained which assures the accuracy of subsequent investigations. First, in this paper, the basic concept of hyperspectral imaging technique and denoising is discussed along with the different categories of noise, their alternative terms, causes. After that, paper describes the various HSI denoising approaches which can be grouped in four sections: 3D model-based approaches and 3D filtering approaches, spectral and spatial-spectral penalty-based approaches, low rank-based approaches, making the mixed noise assumption with their advantages and disadvantages. There are some challenges that remains such as choosing the right models and parameters, managing spectral distortion and band-wise normalization, accurately estimating noise variance, and addressing scenarios involving mixed noise, computational cost. The review offers a useful guide for newcomers, shedding light on denoising strategies and highlighting emerging trends in HSI. This paper contributes also to find what are the previously proposed methods for HSI denoising. How effective they are and what are the limitations of these methods.