  Massive stars live fast and die young. They shine furiously for a few million
years, during which time they synthesize most of the heavy elements in the
universe in their cores. They end by blowing themselves up in a powerful
explosion known as a supernova. During this process, the core collapses to a
neutron star or a black hole, while the outer layers are expelled with
velocities of thousands of kilometers per second. The resulting fireworks often
outshine the entire host galaxy for many weeks.
  The explosion energy is eventually radiated away, but powering of the newborn
nebula continues by radioactive isotopes synthesized in the explosion. The
ejecta are now quite transparent, and we can see the material produced in the
deep interiors of the star. To interpret the observations, detailed spectral
modeling is needed. This thesis aims to develop and apply state-of-the-art
computational tools for interpreting and modeling supernova observations in the
nebular phase. This requires calculation of the physical conditions throughout
the nebula, including non-thermal processes from the radioactivity, thermal and
statistical equilibrium, as well as radiative transport. The inclusion of
multi-line radiative transfer, which we compute with a Monte Carlo technique,
represents one of the major advancements presented in this thesis.
