As a kinetic approach, Wigner equations for quantum transport in nano-devices and their numerical solutions will be discussed in this chapter. First, we address the issues of the phase space truncations for the Wigner distributions in computational simulations and the Frensley inflow boundary conditions at the physical boundaries of the devices. Then, a conservative adaptive spectral element method based on cell averages will be given, followed by an upwinding finite difference method. Numerical results on a resonant tunneling diode (RTD) will be presented using both methods.