Fostered by the possibilities of multi-dimensional computational modeling, in particular the advent of three-dimensional (3D) simulations, our understanding of the neutrino-driven explosion mechanism of core-collapse supernovae (SNe) has experienced remarkable progress over the past decade. First self-consistent, first-principle models have shown successful explosions in 3D, and even failed cases may be cured by moderate changes of the microphysics inside the neutron star (NS), better grid resolution, or more detailed progenitor conditions at the onset of core collapse, in particular large-scale perturbations in the convective Si and O burning shells. 3D simulations have also achieved to follow neutrino-driven explosions continuously from the initiation of the blast wave, through the shock breakout from the progenitor surface, into the radioactively powered evolution of the SN, and towards the free expansion phase of the emerging remnant. Here we present results from such simulations, which form the basis for direct comparisons with observations of SNe and SN remnants in order to derive constraints on the still disputed explosion mechanism. It is shown that predictions based on hydrodynamic instabilities and mixing processes associated with neutrino-driven explosions yield good agreement with measured NS kicks, light-curve properties of SN 1987A, and asymmetries of iron and 44Ti distributions observed in SN 1987A and Cassiopeia A.
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