Context. The well-observed and well-studied type IIP Supernova 1987A (SN 1987A), produced by the explosion of a blue supergiant in the Large Magellanic Cloud, is a touchstone for the evolution of massive stars, the simulation of neutrino-driven explosions, and the modeling of light curves and spectra. Aims. In the framework of the neutrino-driven explosion mechanism, we study the dependence of explosion properties on the structure of different blue supergiant progenitors and compare the corresponding light curves with observations of SN 1987A. Methods. Three-dimensional (3D) simulations of neutrino-driven explosions are performed with the explicit, finite-volume, Eulerian, multifluid hydrodynamics code Prometheus, using of four available presupernova models as initial data. At a stage of almost homologous expansion, the hydrodynamical and composition variables of the 3D models are mapped to a spherically symmetric configuration, and the simulations are continued with the implicit, Lagrangian radiation-hydrodynamics code Crab to follow the blast-wave evolution into the SN outburst. Results. All of our 3D neutrino-driven explosion models, with explosion energies compatible with SN 1987A, produce 56 Ni in rough agreement with the amount deduced from fitting the radioactively powered light-curve tail. Two of our models (based on the same progenitor) yield maximum velocities of around 3000 km s −1 for the bulk of ejected 56 Ni, consistent with observational data. In all of our models inward mixing of hydrogen during the 3D evolution leads to minimum velocities of hydrogen-rich matter below 100 km s −1 , which is in good agreement with spectral observations. However, the explosion of only one of the considered progenitors reproduces the shape of the broad light curve maximum of SN 1987A fairly well. Conclusions. The considered presupernova models, 3D explosion simulations, and light-curve calculations can explain the basic observational features of SN 1987A, except for those connected to the presupernova structure of the outer stellar layers. All progenitors have presupernova radii that are too large to reproduce the narrow initial luminosity peak, and the structure of their outer layers is not suitable to match the observed light curve during the first 30-40 days. Only one stellar model has a structure of the helium core and the He/H composition interface that enables sufficient outward mixing of 56 Ni and inward mixing of hydrogen to produce a good match of the dome-like shape of the observed light-curve maximum, but this model falls short of the helium-core mass of 6 M inferred from the absolute luminosity of the presupernova star. The lack of an adequate presupernova model for the well-studied SN 1987A is a real and pressing challenge for the theory of the evolution of massive stars.