Bioinspired engineering offers a promising alternative approach in accelerating the development of many man-made systems. Next-generation infrared (IR) sensing systems can also benefit from such nature-inspired approach. The inherent compact and uncooled operation of biological IR sensing systems provides ample inspiration for the engineering of portable and high-performance artificial IR sensing systems. This review overviews the current understanding of the biological IR sensing systems, most of which are thermal-based IR sensors that rely on either bolometer-like or photomechanic sensing mechanism. The existing efforts inspired by the biological IR sensing systems and possible future bioinspired approaches in the development of new IR sensing systems are also discussed in the review. Besides these biological IR sensing systems, other biological systems that do not have IR sensing capabilities but can help advance the development of engineered IR sensing systems are also discussed, and the related engineering efforts are overviewed as well. Further efforts in understanding the biological IR sensing systems, the learning from the integration of multifunction in biological systems, and the reduction of barriers to maximize the multidiscipline collaborations are needed to move this research field forward.