Compositions of matter and methods for making, storing and administering artificial blood substitutes. Artificial blood substitutes may have oxygen carriers that encapsulate an oxygen-binding compound in a polymer vesicle. Oxygen-binding compounds may include hemoglobin, myoglobin, or other oxygen binding compounds having characteristics similar to hemoglobin. Oxygen carriers may include nanoparticles, polymers and/or polymersomes comprising of poly(ethylene oxide)-block-poly(ε-caprolactone) (PEO-b-PCL) and related diblock copolymers of poly(ethylene oxide)-block-poly(γ-methyl ε-caprolactone) (PEO-b-PMCL). The oxygen carriers may have tunable oxygen-binding capacities, uniform and appropriately small size distributions, and human bloodlike viscosities and oncotic properties.