Massive and massless potentials play an essential role in the perturbative formulation of particle interactions. Many difficulties arise due to the indefinite metric in gauge theoretic approaches, or the increase with the spin of the UV dimension of massive potentials. All these problems can be evaded in one stroke: modify the potentials by suitable terms that leave unchanged the field strengths, but are not polynomial in the momenta. This feature implies a weaker localization property: the potentials are "string-localized". In this setting, several old issues can be solved directly in the physical Hilbert space of the respective particles: We can control the separation of helicities in the massless limit of higher spin fields and conversely we recover massive potentials with 2 s + 1 degrees of freedom by a smooth deformation of the massless potentials ("fattening"). We construct stress-energy tensors for massless fields of any helicity (thus evading the Weinberg-Witten theorem). We arrive at a simple understanding of the van Dam-Veltman-Zakharov discontinuity concerning, e.g., the distinction between a massless or a very light graviton. Finally, the use of string-localized fields opens new perspectives for interacting quantum field theories with, e.g., vector bosons or gravitons.