The endeavours made in this book are intended to study the effect of material tailoring on the crystallization behaviour, glass forming ability and structure/microstructure of Zr/Cu-based metallic glasses and nanoquasicrystal-glass composites. The substitution of Ga on Al site in Zr-Al-Cu-Ni alloy affects the nucleation and growth characteristics of quasicrystals and consequently changes the morphology of nanoquasicrystals. A new metallic glass composition; Zr-Ga-Cu-Ni with glass transition temperature (Tg); 614 K has been observed. The addition of Ti destabilizes the glassy phase in (Zr-Al-Cu-Ni)Ti alloys. Formation of single quasicrystalline phase by annealing the glass has been found for the alloys. The size of quasicrystal grain decreases with increase of Ti. Rapidly solidified ribbons of Cu-Ga-Mg-Ti and Cu-Al-Mg-Ti alloys show the formation of γ-brass type phase, which is an approximant of quasicrystals. The Cu-Ga-Mg-Ti alloy display ordered γ-brass structure, whereas Cu-Al-Mg-Ti leads to the formation of amorphous and nanocrystalline disordered bcc γ-brass phase. Electron diffraction patterns have been found to show a close structural similarity with the icosahedral phase.