Theoretical predictions for X-ray and gamma-ray emissions from Type Ia supernovae (SNe Ia) are presented based on various models of thermonuclear explosions. X-ray and gamma-ray emissions from supernovae originate mostly from radioactive decays of Ni-56. From normal SNe Ia, the line gamma-rays call be detected with Compton Gamma-Ray Observatory (CGRO) and INTEGRAL satellite if SNe Ia occur within the distance of d < 13 Mpc and 40 Mpc, respectively. For peculiar SNe Ia 1991T, the existence of Ni-56 near the surface, as suggested from optical observations, results in more intense line gamma-ray emission than normal SNe Ia. The line gamma-rays detection from SN 1991T is actually reported by COMPTEL on board CGRO, on days 66 and 136 after the explosion, though OSSE (also on board CGRO) has reported only upper limits. If the distance to SN 1991T is d similar to 17 Mpc, the observed intensity is 2 - 3 times larger than that predicted from the explosion models for SN 1991T. This implies that the distance is as short as similar to 13 Mpc or the white dwarf had a super Chandrasekhar mass if d similar to 17 Mpc. If Ni-56 is, indeed synthesized near the surface of SN 1991T, the 812 keV line from the Ni-56 decay and the 847 keV line from the Co-56 decay can be observed with INTEGRAL satellite if a similar supernova occurs at d less than or similar to 50 Mpc. We also make predictions for the line gamma-ray intensities from the Ti-44 decay in young nearby supernova remnants (SNRs). In view of the uncertainties in the synthesized mass of Ti-44 is as well as the uncertain half life of Ti-44, it is possible to detect line gamma-rays from nearby SNRs. In fact, the Ti-44 line gamma-ray from Cas A has already been detected with COMPTEL, though OSSE has reported negative detections. These observations provide constraints on the nucleosynthesis models of core-collapse supernovae. The detection of line gamma-rays from SNRs such as Tycho and Kepler would be critical to clear the nature of explosions.