  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.
