Sustaining the vital functions of cells outside the organism requires strictly defined parameters. In order to ensure their optimal growth and development, it is necessary to provide a range of nutrients and regulators. Hydrogels are excellent materials for 3D in vitro cell cultures. Their ability to retain large amounts of liquid, as well as their biocompatibility, soft structures, and mechanical properties similar to these of living tissues, provide appropriate microenvironments that mimic extracellular matrix functions. The wide range of natural and synthetic polymeric materials, as well as the simplicity of their physico-chemical modification, allow the mechanical properties to be adjusted for different requirements. Sodium alginate-based hydrogel is a frequently used material for cell culture. The lack of cell-interactive properties makes this polysaccharide the most often applied in combination with other materials, including gelatin. The combination of both materials increases their biological activity and improves their material properties, making this combination a frequently used material in 3D printing technology. The use of hydrogels as inks in 3D printing allows the accurate manufacturing of scaffolds with complex shapes and geometries. The aim of this paper is to provide an overview of the materials used for 3D cell cultures, which are mainly alginate–gelatin hydrogels, including their properties and potential applications.