Quasicrystals, related to irrational numbers, are important space-filling structures without decay nor translational invariance. How to numerically compute the incommensurate system presents a big challenge. In the past years, some accurate and efficient methods of quasicrystals have been proposed. In this talk, we will review the recent development of these methods, including periodic approximation method, projection method, and finite point recovery method. The corresponding convergence analysis will also be reported. If time allows, we will introduce some applications by using these numerical methods, including soft-matter quasicrystals, grain boundaries, quasicrystal phase transition, quasiperiodic homogenized problems, quasiperiodic Schrodinger systems.