The engineering of tissues under a three-dimensional (3D) microenvironment is a great challenge and needs a suitable supporting biomaterial-based scaffold that may facilitate cell attachment, spreading, proliferation, migration, and differentiation for proper tissue regeneration or organ reconstruction. Polysaccharides as natural polymers promise great potential in the preparation of a three-dimensional artificial extracellular matrix (ECM) (i.e., hydrogel) via various processing methods and conditions. Natural polymers, especially gums, based upon hydrogel systems, provide similarities largely with the native ECM and excellent biological response. Here, we review the origin and physico-chemical characteristics of potentially used natural gums. In addition, various forms of scaffolds (e.g., nanofibrous, 3D printed-constructs) based on gums and their efficacy in 3D cell culture and various tissue regenerations such as bone, osteoarthritis and cartilage, skin/wound, retinal, neural, and other tissues are discussed. Finally, the advantages and limitations of natural gums are precisely described for future perspectives in tissue engineering and regenerative medicine in the concluding remarks.