Asymmetry in the innermost part of the supernova (SN) ejecta is a key to understanding their explosion mechanisms. Late-time spectroscopy is a powerful tool to investigate the issue. We show what kind of geometry is inferred for different types of SNe – core-collapse SNe Ib/c, those associated with Gamma-Ray Bursts (GRBs), and thermonuclear SNe Ia –, and discuss implications for the explosion mechanisms, observational diversities, and cosmological applications. For SNe Ib/c, the data show the clear deviation from spherical symmetry, and they are most consistent with the bipolar-type explosion as the characteristic geometry. Detailed modeling of optical emissions from SN 1998bw associated with GRB980425 indicates that this SN was in the extreme end of the bipolar explosion, suggesting that the explosion mechanisms of canonical SNe Ib/c and GRB-SNe are different. The situation is different for SNe Ia. Late-time spectra indicate the deviation from spherical symmetry, but for SNe Ia the explosion is asymmetric between two hemispheres, i.e., one-sided explosions. The diversities arising from different viewing directions can nicely explain (a part of) observational diversities of SNe Ia, and correcting this effect may improve the standard-candle calibration of SNe Ia for cosmology.