Main difficulties of numerically solving the 3D time-dependent Navier-Stokes equations are incompressibility condition, nonlinearity and longtime integration. First, we discuss the research progress and recent achievements in the highly efficient fully discrete finite element method for solving the 3D time-dependent Navier-Stokes equations. Secondly, we expound the stability and error estimates of the finite element spatial discrete solution and the optimal error estimates of the highly efficient fully discrete finite element method for solving the 3D time-dependent Navier-Stokes equations.