Cells respond to a variety of stimuli, including biochemical, topographical and mechanical signals originating from their micro-environment. Cell responses to the mechanical properties of their substrates have been increasingly studied for about 14 years. To this end, several types of materials based on synthetic and natural polymers have been developed. Presentation of biochemical ligands to the cells is also important to provide additional functionalities or more selectivity in the details of cell/material interaction. In this review article, we will emphasize the development of synthetic and natural polymeric materials with well-characterized and tunable mechanical properties. We will also highlight how biochemical signals can be presented to the cells by combining them with these biomaterials. Such developments in materials science are not only important for fundamental biophysical studies on cell/material interactions but also for the design of a new generation of advanced and highly functional biomaterials.