Since early 1900s, a number of technical breakthroughs in electronics and photonics have started to bring terahertz(THz) wave technologies from laboratory demonstrations to industrial applications such as non-destructive testing, security, medicine, communications, etc. Recent advances in producing THz radiation have stimulated interests in studying the interaction between radiation and biological molecules and tissue. Despite this emerging ubiquity of THz applications, relatively little is known about the effect of THz radiation on biological systems. It is clear that the non-thermal mechanisms by which the non-ionizing THz radiation influences biological functions must be fundamentally different from those at play when high-energy(UV, X-ray, gamma, et al) radiation interacts and damages bio-matter. The latest application progresses of terahertz technique on biomedicine are overviewed by two parts：advances in characterization techniques and biological effects. Furthermore，the future trends and the key scientific problems of THz-biomedicine are also pointed out.