We investigate experimentally the effects of pore size, surface wettability, and penetration mode on the characteristics of liquid penetration through meshes. Utilizing the impact of droplets and the hydrostatic pressure, we study water penetration through superhydrophobic, hydrophobic, superhydrophilic, and hydrophilic meshes with different uniform radii and pitch values of the pores. In the case of dynamic penetration enabled by the droplet impact, our results show that surface wettability has a negligible effect on either the threshold speed of the droplet penetration or the penetrating liquid mass. The threshold droplet speed is found to be mainly determined by the synergistic effects of global and local dynamic pressures of the impacting droplet, and a modified expression for the threshold droplet speed is proposed. For the quasi-static penetration based on the applied hydrostatic pressure, we find that surface wettability and pore pitch do not affect the penetration threshold pressure but do affect the pressure at which the liquid penetration ceases. This is due to the fact that under quasi-static conditions, the droplet liquid spreads out and merges with that at the adjacent pores on the mesh underside, affecting the wetted area and, hence, the capillary pressure resisting penetration.