With the standardization of 5G, commercial millimeter wave (mmWave) communications has become a reality despite all the concerns about the unfavorable propagation characteristics of these frequencies. Even though the 5G systems are still being rolled out, it is argued that their gigabits per second rates may fall short in supporting many emerging applications, such as 3D gaming and extended reality. Such applications will require several hundreds of gigabits per second to several terabits per second data rates with low latency and high reliability, which are expected to be the design goals of the next generation 6G communications systems. Given the potential of terahertz (THz) communications systems to provide such data rates over short distances, they are widely regarded to be the next frontier for the wireless communications research. The primary goal of this chapter is to equip readers with sufficient background about the mmWave and THz bands so that they are able to both appreciate the necessity of using these bands for commercial communications in the current wireless landscape and to reason the key design considerations for the communications systems operating in these bands. Towards this goal, this chapter provides a unified treatment of these bands with particular emphasis on their propagation characteristics, channel models, design and implementation considerations, and potential applications to 6G wireless. A brief summary of the current standardization activities related to the use of these bands for commercial communications applications is also provided.