In the emerging field of tissue engineering and regenerative medicine, new viable and functional tissue is fabricated from living cells cultured on an artificial matrix in a simulated biological environment. It is evident that the specific requirements for the three main components, cells, scaffold materials, and the culture environment, are very different, depending on the type of cells and the organ‐specific application. Identifying the variables within each of these components is a complex and challenging assignment, but there do exist general requirements for designing and fabricating tissue engineering scaffolds. Therefore, this review explores one of the three main components, namely, the key concepts, important parameters, and required characteristics related to the development and evaluation of tissue engineering scaffolds. An array of different design strategies will be discussed, which include mimicking the extra cellular matrix, responding to the need for mass transport, predicting the structural architecture, ensuring adequate initial mechanical integrity, modifying the surface chemistry and topography to provide cell signaling, and anticipating the material selection so as to predict the required rate of bioresorption. In addition, this review considers the major challenge of achieving adequate vascularization in tissue engineering constructs, without which no three‐dimensional thick tissue such as the heart, liver, and kidney can remain viable.