With one- and two-dimensional particle-in-cell (PIC) codes, we simulate the generation of high power terahertz (THz) emission from the interaction of ultrashort intense lasers with tenuous plasma and gas targets. By driving high-amplitude electron plasma waves either with a laser wakefield or the beatwave of two laser pulses, powerful THz electromagnetic pulses can be produced by linear mode conversion in inhomogeneous plasma or by the transient current induced at the surfaces of a thin plasma layer of few plasma wavelengths. Even with incident lasers at moderate intensity such as 10¹⁷W/cm², the produced emission can be at the level of tens of MW in power and capable of affording field strengths of a few MV/cm, suitable for the studies of THz nonlinear physics. With field ionization included in the PIC codes, THz emission from laser interaction with tenuous gas targets is simulated. It is found that the transient transverse current formed during the ionization processes is responsible for the THz emission. With this mechanism, one may also obtain THz fields of MV/cm at lower laser intensity as compared with the schemes of plasma-wave excitation.