Over the last three decades, proteins and peptides have attracted great interest as drugs of choice for combating a broad spectrum of diseases, including diabetes mellitus, cancer, and infectious and neurological diseases. However, the delivery of therapeutic proteins to target sites should take into account the obstacles and limitations related to their intrinsic sensitivity to different environmental conditions, fragile tertiary structures, and short half-life. Polymeric nanostructures have emerged as competent vehicles for protein delivery, as they are multifunctional and can be tailored according to their peculiarities. Thus, the enhanced bioavailability and biocompatibility, the adjustable control of physicochemical features, and the colloidal stability of polymer-based nanostructures further enable either the embedding or conjugation of hydrophobic or hydrophilic bioactive molecules, which are some of the features of paramount importance that they possess and which contribute to their selection as vehicles. The present review aims to discuss the prevalent nanostructures composed of block copolymers from the viewpoint of efficient protein hospitality and administration, as well as the up-to-date scientific publications and anticipated applications of polymeric nanovehicles containing proteins and peptides.