Transmission electron microscopy and first-principles calculations are integrated to investigate the crystal structures and the microstructures of titanium-based intermetallics and ceramics on the nanometer, atomic, and electronic scales. The thesis contains three parts. (1) Distribution of W and the precipitation mechanism of the B2 phase in the lamellar structure of a TiAl alloy. The B2-stabilizing effect of W and its site preference can be explained well on the basis of the pseudo-gap effect and the strong covalent W-Ti bonding. (2) The polymorphism, electronic structure, and microstructure of Ti3SiC2. Unconventional stacking faults have been identified, which result from insertion of additional TiC layers into normal Ti3SiC2 crystal, instead of from the dissociation of dislocations as occurs in most materials. (3) The effect of alloying elements Si and Al on the twin boundary energy of TiC. It was found that Si and Al can reduce the twin boundary energy of TiC, leading to the formation of a lot of microtwins.