We study perturbative and non-perturbative aspects of heavy-quark fragmentation into hadrons, emphasizing the large-x region, where x is the energy fraction of the detected hadron. We first prove that when the moment index N and the quark mass m get large simultaneously with the ratio (N Lambda/m) fixed, the fragmentation function depends on this ratio alone. This opens up the way to formulate the non-perturbative contribution to the fragmentation function at large N as a shape function of m(1-x) which is convoluted with the Sudakov-resummed perturbative result. We implement this resummation and the parametrization of the corresponding shape function using Dressed Gluon Exponentiation. The Sudakov exponent is calculated in a process independent way from a generalized splitting function which describes the emission probability of an off-shell gluon off a heavy quark. Non-perturbative corrections are parametrized based on the renormalon structure of the Sudakov exponent. They appear in moment space as an exponential factor, with a leading contribution scaling as (N Lambda/m) and corrections of order (N Lambda/m)^3 and higher. Finally, we analyze in detail the case of B-meson production in e+e- collisions, confronting the theoretical predictions with LEP experimental data by fitting them in moment space.