Artificial repetitive polypeptides have grown in popularity as a bioinspired alternative to synthetic polymers. The genetically encoded synthesis, monodispersity, potential lack of toxicity, and biocompatibility are attractive features of these biopolymers for biological applications. Elastin-like polypeptides (ELPs) are one such class of biopolymers that are of particular interest because of their "smart"-stimuli responsive-properties. Herein, we discuss the genetically encoded design and recombinant synthesis of ELPs that enable precise control of their physicochemical properties and which have led to a wide range of biomedical applications of these biopolymers in the last decade.