The depletion theory of nanoparticles immersed in a semidilute polymer solution is reinterpreted in terms of depleted chains of polymer segments. Limitations and extensions of mean-field and scaling theories are discussed. An explicit expression for the interaction between two small spheres is also reviewed. The depletion free energy for a particle of general shape is given in terms of the capacitance or effective Stokes radius. This affords a reasonable explanation for the effect of polymer on protein precipitation.