Recent development of intense terahertz (THz) pulse generation technique has offered novel opportunities to reveal ultrafast phenomena in a variety of materials on tabletop experiments and provided a new pathway toward ultrafast control of quantum phases. Here we present our recent study of nonequilibrium dynamics in metallic superconductors NbN excited by intense THz pulse. Since the superconducting gap energy is located in the THz frequency range, the intense THz pulse excitation makes it possible to instantaneously excite high-density quasiparticles at the gap edge without injecting excess energies. It has also become possible to coherently drive the superconducting ground state without exciting incoherent quasiparticles by tuning the pump frequency below the gap energy. The ultrafast dynamics of the order parameter induced by such an intense low energy excitation is directly probed, and the nature of a collective excitation, namely the Higgs amplitude mode, is revealed. Efficient THz higher-harmonic generation from a superconductor is discovered, manifesting the nonlinear coupling between the THz wave and the Higgs mode. We also report the experimental results in a multi-gap superconductor MgB2.