The terahertz (THz) band is expected to play a more important role in 6G communication networks. It can provide large bandwidth and high-speed transmission rate to support prospective 6G scenarios from space to ground and from macro-scale to nano-scale. However, the THz channel characteristics vary greatly for different scenarios. This article presents a multi-dimensional overview of propagation channel characteristics and modeling for potential THz communication scenarios, including ground, space, and nano-scale communications. The atmospheric attenuation and propagation mechanisms are first discussed for ground scenarios. Then the channel measurements, characteristics, and models for specific ground scenarios, including indoor office, data center, kiosk, smart rail, and massive MIMO, are investigated. Following this, the THz space communication channels are summarized according to the satellite altitude. Futhermore, THz nano-scale communication channels including on-chip and body-centric are analyzed. Finally, future research challenges are outlined.