The sensational discovery of quasicrystals with fivefold rotational symmetry and no periodic translation order ten years ago made a strong impact to all solid state sciences based on crystals and crystallography, comprising metallurgy, materials science，chemistry，physics, mineralogy，etc. After a decennium of intensive study，many important aspects of this new class of materials and a new kind of ordered state with the so-called "forbidden" symmetry and quasiperiodicity have been made clear. Time is perhaps ripen to review the main advances of quasicrystal research made in the past ten years. The topics discussed in the present review arc:(1)quasicrystal or five-fold twins? (2)why fivefold symmetry? (3)why quasiperiodicity?(9 ) stable quasicrystals;(5)crystalline approximants.