The synthesis of quasicrystalline phases in complex metallic alloys appears to be advantageous for fundamental research as well as practical application. Studies on quasicrystals and their applications have been research frontiers in chemistry, physics, mathematics, materials science and metallurgy in the past few decades. The remarkable progress has been made in the formation, growth and phase stability, structure and modeling, mathematics of quasiperiodic and a periodic structures, physical properties (transport, magnetic, dynamical, mechanical etc.), surfaces and over layers, applications etc. However, the structural solution of the quasicrystal is still under debate and it will provide a broad aspect for future development and guide the investigations of different aspects of quasicrystals. Therefore, a review on the quasicrystal may be attractive for material science & engineering community.