Fractional calculus has become a basic tool for modeling phenomena involving memory. However, due to the non-local nature of fractional derivatives, the computations involved in solving a fractional differential equations (FDEs) are tedious and time consuming. Developing numerical and analytical methods for solving nonlinear FDEs has been a subject of intense research at present. In the present article, we review some of the existing numerical methods for solving FDEs and some new methods developed by our group recently. We also perform their comparative study.