Biomedical applications—prostheses, tissue engineering, drug delivery, and wound healing—demand increasingly sophisticated characteristics from the materials that come into contact with living systems in the laboratory and the clinic. With the development of microfluidics, there is an opportunity to create active biomaterials based on embedded microfluidic structures. These structures allow for control of the concentrations of soluble chemicals and hydrodynamic stresses within the material and at its interfaces, and thus allow one to tailor the environment experienced by the living tissue. In this article, we review initial efforts to develop these microfluidic biomaterials and present considerations regarding the required characteristics of the materials and of the microfluidic-mediated mass transfer. As specific examples, we present work toward microfluidic control of mass transfer in scaffolds for tissue engineering and in wound dressings.