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, accurate and efficient methods of quasicrystals have been developed. In this talk, we firstly give the periodic approximation method and projection method, as will as the corresponding convergence analysis. Then, we will introduce some applications by using these numerical methods, including soft-matter quasicrystals, grain boundaries, quasicrystal phase transition, quasiperiodic homogenized problems. Finally, if time allows, we will present a new approach, the finite point recovery method, to address non-smooth quasicrystals.