Recent changes in how people consume multimedia services are causing an explosive increase in mobile traffic. With more and more people using wireless networks, the demand for the ultra-fast wireless communications systems is increasing. To date, this demand has been accommodated with advanced modulation schemes and signal-processing technologies at microwave frequencies. However, without increasing the carrier frequencies for more spectral resources, it may be quite difficult to keep up with the needs of users. Although there are several alternative bands, recent advances in terahertz-wave (THz-wave) technologies have attracted attention due to the huge bandwidth of THz waves and its potential for use in wireless communications. The frequency band of 275 ~ 3000 GHz , which has not been allocated for specific uses yet, is especially of interest for future wireless systems with data rates of 10 Gb/s or higher. Although THz communications is still in a very early stage of development, there have been lots of reports that show its potential. In this review, we will examine the current progress of THz-wave technologies related to communications applications and discuss some issues that need to be considered for the future of THz communications.