Core collapse supernovae (SN) are the final stages of stellar evolution in massive stars during which the central region collapses, forms a neutron star (NS), and the outer layers are ejected. Recent explosion scenarios assumed that the ejection is due to energy deposition by neutrinos into the envelope, but detailed models do not produce powerful explosions. There is new and mounting evidence for an asphericity and, in particular, for axial symmetry in several supernovae which may be hard to reconcile within the spherical picture. This evidence includes the observed high polarization and its variation with time, pulsar kicks, high velocity iron-group and intermediate-mass elements material observed in remnants, direct observations of the debris of SN 1987A, etc. Some of the new evidence is discussed in more detail. To be in agreement with the observations, any successful mechanism must invoke some sort of axial symmetry for the explosion. We consider jet-induced/dominated explosions of core collapse supernovae. Our study is based on detailed 3-d hydrodynamical and radiation transport models. We find that the observations can be explained by low velocity, massive jets which stall well within the SN envelope. Such outflows may be produced by MHD-mechanisms, convective dominated accretion disks on the central object or asymmetric neutrino emissions. Asymmetric density/chemical distributions and, for SN 2002ap, off-center energy depositions have been identified as crucial for the interpretation of the polarization.