In this work, a brief overview on the recent stability results of fractional differential equations and the analytical methods used is given. The stability of the linear fractional system by analyzing the eigenvalues is discussed. Also the stability of the nonlinear fractional dynamical system is analyzed by giving conditions on the nonlinear term. Further the stability of fractional neutral and integrodifferential systems is studied. To show the applicability of fractional differential equations, some examples were presented.