Bound states in the continuum (BIC) is a completely bound resonance with its frequency within the continuum spectrum. It has an infinite Q factor,and strong light-matter interaction. The BIC phenomenon is critical for developing functional devices. The introduction of BIC mechanism in terahertz metasurface provides a new way to customize high Q resonance. In this review, the classification, formation mechanism, and main properties of BIC are briefly introduced, and the emerging applications of BIC in terahertz metasurfaces, such as high sensitivity sensing, chiral enhancement, spectral coding, and near-field imaging, are emphasized. In addition, BIC carries topological charges that are defined by the winding number of the polarization vector, such charges can only be created or annihilated by drastically changing the system parameters. The topological properties of BIC also provide new possibilities for the discovery of new phenomena in topological photonics. In the future, BIC can bring more developments in the field of optics and photonics.