Tissue Engineering is a promising emerging field that studies the intrinsic regenerative potential of the human body and uses it to restore functionality of damaged organs or tissues unable of self-healing due to illness or ageing. In order to achieve regeneration using Tissue Engineering strategies, it is first necessary to study the properties of the native tissue and determine the cause of tissue failure; second, to identify an optimum population of cells capable of restoring its functionality; and third, to design and manufacture a cellular microenvironment in which those specific cells are directed towards the desired cellular functions. The design of the artificial cellular niche has a tremendous importance, because cells will feel and respond to both its biochemical and biophysical properties very differently. In particular, the artificial niche will act as a physical scaffold for the cells, allowing their three-dimensional spatial organization; also, it will provide mechanical stability to the artificial construct; and finally, it will supply biochemical and mechanical cues to control cellular growth, migration, differentiation and synthesis of natural extracellular matrix. During the last decades, many scientists have made great contributions to the field of Tissue Engineering. Even though this research has frequently been accompanied by vast investments during extended periods of time, yet too often these efforts have not been enough to translate the advances into new clinical therapies. More and more scientists in this field are aware of the need of rational experimental designs before carrying out complex, expensive and time-consuming in vitro and in vivo trials. This review highlights the importance of computer modeling and novel biofabrication techniques as critical key players for a rational design of artificial cellular niches in Tissue Engineering.