There are many lines of evidence for anisotropy at all scales in the explosions of core collapse supernovae, e.g. visual inspection of the images of resolved supernova remnants, polarization measurements, velocity profiles, "natal kicks" of neutron stars, or spectroscopic observations of different regions of remnants. Theoretical stability considerations and detailed numerical simulations have shown that Rayleigh-Taylor (RT) instabilities arise in the star after the explosion, which leads to the early fragmentation of parts of the ejecta. The clumps thus created are of interest to a variety of topics, one of them being the formation environment of the solar system. There is a high probability that the solar system formed in the vicinity of a massive star that, shortly after its formation, exploded as a core collapse supernova. As argued in this thesis as well as other works, a core collapse supernova generally is a good candidate for chemically enriching the forming solar system with material. As forming proto--planetary systems in general have a high probability of being contaminated with supernova material, a method was developed for detecting tracer elements indicative supernova contamination in proto--planetary systems.The degree of the anisotropy of the supernova explosion can have dramatic effects on the mode of delivery of that material to the solar system, or proto--planetary systems in general. Thus it is of particular interest to be able to predict the structure of the supernova ejecta. Numerical simulations of the explosions of core collapse supernovae were done in 3 dimensions in order to study the formation of structure. It is found that RT instabilities result in clumps in the He- and C+O rich regions in the exploding star that are overdense by 1-2 orders of magnitude. These clumps are potential candidates for enriching the solar system with material. In the course of the further evolution of the supernova remnant, these RT clumps are likely to evolve into ejecta knots of the type observed in the Cassiopeia A supernova remnant.