Tissue engineering has shown great promise in developing novel therapies for treating injured tissue and organ failure. Scaffolds play a pivotal role in tissue engineering. Biodegradable polymers are the primary choice of material for tissue engineering scaffolds, due to their numerous advantageous properties. In this article, the principles of tissue engineering are discussed in relation to polymer science and engineering. The most frequently used polymers in tissue engineering are briefly reviewed. These include synthetic and natural polymers commonly used in constructing both porous and hydrogel scaffolds. Their structure and critical properties in relation to scaffold function are discussed in depth, along with a detailed review of the important roles functionalized materials and controlled release play in tissue engineering. Important polymer processing techniques in the context of scaffold fabrication are also reviewed. These include the textile technologies, electrospinning, particulate‐leaching techniques, phase‐separation techniques, rapid prototyping, and other novel three‐dimensional (3D) fabrication techniques. In this update, the impact of pluripotent stem cells, conductive polymers, controlled drug release, 3D printing, and nanofibrous topology on tissue engineering are also discussed.