One of the main issues of hyperspectral imaging data is to unravel the relevant, yet overlapped, huge amount of information contained in the spatial and spectral dimensions. When dealing with the application of multivariate models in such high-dimensional data, sparsity can improve the interpretability and the performance of the model. In this chapter, we will introduce the exploration of hyperspectral images using a sparse version of the well-known principal component analysis method to demonstrate how the derived models can reveal very useful spectral zones. In particular, we will present two practical applications related to different issues: the separation among groups of homogeneous samples and the identification of outlier pixels in the spatial domain. For both case studies, guidance to the identification of the proper level of sparsity will be provided and, furthermore, we will show how sparsity can improve the chemical interpretation of the results