The search for understanding the interactions of nanosized materials with living organisms is leading to the rapid development of key applications, including improved drug delivery by targeting nanoparticles, and resolution of the potential threat of nanotechnological devices to organisms and the environment. Unless they are specifically designed to avoid it, nanoparticles in contact with biological fluids are rapidly covered by a selected group of biomolecules to form a corona that interacts with biological systems. Here we review the basic concept of the nanoparticle corona and its structure and composition, and highlight how the properties of the corona may be linked to its biological impacts. We conclude with a critical assessment of the key problems that need to be resolved in the near future.