Elastin-like recombinant protein polymers are a new family of polymers which are captivating the attention of a broad audience ranging from nanotechnologists to biomaterials and more basic scientists. This is due to the extraordinary confluence of different properties shown by this kind of material that are not found together in other polymer systems. Elastin-like polymers are extraordinarily biocompatible, acutely smart and show uncommon self-assembling capabilities. Additionally, they are highly versatile, since these properties can be tuned and expanded in many different ways by substituting the amino acids of the dominating repeating peptide or by inserting, in the polymer architecture, (bio)functional domains extracted from other natural proteins or de novo designs. Recently, the potential shown by elastin-like polymers has, in addition, been boosted and amplified by the use of recombinant DNA technologies. By this means, complex molecular designs and extreme control over the amino-acid sequence can be attained. Nowadays, the degree of complexity and control shown by the elastin-like protein polymers is well beyond the reach of even the most advanced polymer chemistry technologies. This will open new possibilities in obtaining synthetic advanced bio- and nanomaterials. This review explores the present development of elastin-like protein polymers, with a particular emphasis for biomedical uses, along with some future directions that this field will likely explore in the near future.