Deciphering cell-type composition is critical for charting single-cell spatial maps and cellular atlases of organisms. Most Spatial Transcriptomics (ST) data lack single-cell resolution, computational deconvolution methods have emerged to characterize the composition and spatial heterogeneity of different cell types within spots and tissues. To date, various cell-type deconvolution methods have been developed, each exhibiting its own distinct advantages. To conduct a comprehensive review of these methods, we first provide a formal description of the deconvolution problem. Then, we analyze the advantages and pitfalls of these methods based on their mathematical models. We further discuss related downstream analyses, potential applications, and future directions. In summary, our review aims to guide researchers in gaining an in-depth understanding of the spatial deconvolution problem, enabling them to make informed choices in spatial analysis and advance research on related fields, such as the developmental biology, tumor microenvironment, disease pathology, and clinical treatments.