Since the work of Polder and Van Hove, significant progress has been made in predicting NFRHT. Theoretical formalisms involving trace formulas, fluctuating surface currents, and dyadic Green's functions, have all been developed. Though identical in result, each formalism can be more or less convenient when applied to different situations. Exact solutions for NFRHT between two spheres, ensembles of spheres, a sphere and a half-space, and concentric cylinders have all been determined using these various formalisms. NFRHT in other geometries has been addressed primarily through finite element methods. Meshed surface and volume methods have been developed which handle arbitrary geometries. Alternatively, curved surfaces can be discretized into pairs of flat surfaces and approximated to exchange energy like two semi-infinite half spaces using a thermal proximity approximation (sometimes referred to as the Derjaguin approximation). In systems of small particles, the discrete dipole approximation can be applied.