Polymers are sustainable and renewable materials that are in high demand due to their excellent properties. Natural and synthetic polymers with high flexibility, good biocompatibility, good degradation rate, and stiffness are widely used for various applications, such as tissue engineering, drug delivery, and microfluidic chip fabrication. Indeed, recent advances in microfluidic technology allow the fabrication of polymeric matrix to construct microfluidic scaffolds for tissue engineering and to set up a well-controlled microenvironment for manipulating fluids and particles. In this review, polymers as materials for the fabrication of microfluidic chips have been highlighted. Successful models exploiting polymers in microfluidic devices to generate uniform particles as drug vehicles or artificial cells have been also discussed. Additionally, using polymers as bioink for 3D printing or as a matrix to functionalize the sensing surface in microfluidic devices has also been mentioned. The rapid progress made in the combination of polymers and microfluidics presents a low-cost, reproducible, and scalable approach for a promising future in the manufacturing of biomimetic scaffolds for tissue engineering.