Abstract: The production of Higgs boson pairs at hadron colliders may allow for direct measurements of the trilinear Higgs coupling in the future. Deriving reliable theoretical predictions for this process is, however, uniquely challenging because it is induced by loops of heavy quarks instead of tree-level couplings. Only recently a full fixed-order NLO prediction has become available and thus led to a significant reduction in theoretical uncertainties. For a reliable description of the event kinematics and for the simulation of QCD radiation that will accompany the production of Higgs pairs it is however necessary to supplement such a calculation with parton shower effects. In this talk I will discuss in detail the origin and the impact of associated uncertainties. A key result of the study I will present are surprisingly large uncertainties in phase space regions that one would naively expect not to be affected by parton shower effects.