Black hole-neutron star binary mergers are the one of most promising sources of gravitational waves for next generation ground-based gravitational-wave detectors such as Advanced LIGO, Advanced VIRGO, and KAGRA, and gravitational waves from black hole-neutron star binary are expected to be detected in a next decade. Black hole-neutron star binary mergers have also been proposed as the progenitor of short gamma-ray-bursts in the so-called merger scenario. Moreover, some part of neutron-rich material of the neutron star is ejected dynamically during the merger, and the emission powered by decay of radioactive nuclei would occur (Kilonova/Macronova), which reflect the property of the binary. In this talk, I will discuss dependence of the gravitational waveform, the disk formation and the mass ejection from black hole-neutron star binary merger on the mass ratio of the binary, the equation of state of the neutron star and the black hole spin, which have been clarified by the numerical relativity simulations. In particular, I will focus on the case that the black hole spin is misaligned with the orbital angular momentum of the binary, and discuss the effects of the spin misalignment on the merger process.