Tissue engineering applications commonly encompass the use of three-dimensional (3D) scaffolds to provide a suitable microenvironment for the incorporation of cells or growth factors to regenerate damaged tissues or organs. These scaffolds serve to mimic the actual in vivo microenvironment where cells interact and behave according to the mechanical cues obtained from the surrounding 3D environment. Hence, the material properties of the scaffolds are vital in determining cellular response and fate. These 3D scaffolds are generally highly porous with interconnected pore networks to facilitate nutrient and oxygen diffusion and waste removal. This review focuses on the various fabrication techniques (e.g., conventional and rapid prototyping methods) that have been employed to fabricate 3D scaffolds of different pore sizes and porosity. The different pore size and porosity measurement methods will also be discussed. Scaffolds with graded porosity have also been studied for their ability to better represent the actual in vivo situation where cells are exposed to layers of different tissues with varying properties. In addition, the ability of pore size and porosity of scaffolds to direct cellular responses and alter the mechanical properties of scaffolds will be reviewed, followed by a look at nature's own scaffold, the extracellular matrix. Overall, the limitations of current scaffold fabrication approaches for tissue engineering applications and some novel and promising alternatives will be highlighted.