Although the neutrino is the most abundant known massive particle in the universe, many of its most basic properties are still unknown. This includes not only, e. g., the question whether neutrinos are Dirac or Majorana particles (in the latter case their own anti-particles), but even such a seemingly simple observable as its rest mass. In fact, while the neutrinos were supposed to be mass-less according to the standard model until the 1990s (and thus according to most text books at that time), the experimental confirmation of neutrino oscillations has proven that they possess a non-zero mass (and that mass eigenstates are not identical to the flavor states). The most accurate purely kinematical determination of an upper limit on the neutrino mass, more accurately the mass eigenstate corresponding to an electronic antineutrino, stems from tritium neutrino-mass experiments. In such experiments, the kinetic-energy distribution of the ? electrons emitted in the radioactive decay of molecular tritium is analyzed. Very recently, the Karlsruhe neutrino experiment KATRIN has provided the so far lowest upper bound to the neutrino mass (m??<?0.9?eV?c–2?at 90% confidence level), for the first time breaking the (“magic”) 1 eV c–2 threshold [1]. Since the energy released in the ? decay is not only shared by the emitted (and measured) electron and the neutrino, but also by the remaining molecular ion 3HeT+, the analysis of an experiment like KATRIN requires the very precise knowledge with which probability which amount of energy is left in this ion, the so-called molecular final-state distribution. So far, this information is only available from theoretical calculations. After a brief introduction into the KATRIN experiment, this talk will discuss the challenges in precisely calculating the molecular final-states distribution and in quantifying the uncertainty of the finally extracted neutrino mass due to limitations in the calculation of this distribution.