Although historically, the traditional bidimensional in vitro cell system has been widely used in research, providing much fundamental information regarding cellular functions and signaling pathways as well as nuclear activities, the simplicity of this system does not fully reflect the heterogeneity and complexity of the in vivo systems. From this arises the need to use animals for experimental research and in vivo testing. Nevertheless, animal use in experimentation presents various aspects of complexity, such as ethical issues, which led Russell and Burch in 1959 to formulate the 3R (Replacement, Reduction, and Refinement) principle, underlying the urgent need to introduce non-animal-based methods in research. Considering this, three-dimensional (3D) models emerged in the scientific community as a bridge between in vitro and in vivo models, allowing for the achievement of cell differentiation and complexity while avoiding the use of animals in experimental research. The purpose of this review is to provide a general overview of the most common methods to establish 3D cell culture and to discuss their promising applications. Three-dimensional cell cultures have been employed as models to study both organ physiology and diseases; moreover, they represent a valuable tool for studying many aspects of cancer. Finally, the possibility of using 3D models for drug screening and regenerative medicine paves the way for the development of new therapeutic opportunities for many diseases.