The discovery of fluorescent proteins has inspired a lot of interest to develop synthetic polymers with similar structures and functionalities. In this review article, we first give a brief introduction for the discovery, the structural characteristics and optical properties of fluorescent proteins, using green fluorescent protein (GFP) as an example. In the body part of article, we summarize recent advances in molecular design, synthesis and processing of bioinspired fluorescent polymers with unique optical properties such as high fluorescence quantum yield and robust photostability. Several major approaches highlighted here include the recombination of organic chromophores and proteins, and synthesis of the bioinspired polymers containing a single fluorophore in each polymer chain. The optical properties and applications of some representative bioinspired fluorescent polymers in bioimaging, sensing and imaging-guided therapy are also elucidated.