The Terahertz (THz) band (0.3-3.0 THz), spans a great portion of the Radio Frequency (RF) spectrum that is mostly unoccupied and unregulated. It is a potential candidate for application in Sixth-Generation (6G) wireless networks, as it has the capabilities of satisfying the high data rate and capacity requirements of future wireless communication systems. Profound knowledge of the propagation channel is crucial in communication systems design, which nonetheless is still at its infancy, as channel modeling at THz frequencies has been mostly limited to characterizing fixed Point-to-Point (PtP) scenarios up to 300 GHz. Provided the technology matures enough and models adapt to the distinctive characteristics of the THz wave, future wireless communication systems will enable a plethora of new use cases and applications to be realized, in addition to delivering higher spectral efficiencies that would ultimately enhance the Quality-of-Service (QoS) to the end user. In this paper, we provide an insight into THz channel propagation characteristics, measurement capabilities, and modeling techniques for 6G communication applications, along with guidelines and recommendations that will aid future characterization efforts in the THz band. We survey the most recent and important measurement campaigns and modeling efforts found in literature, based on the use cases and system requirements identified. Finally, we discuss the challenges and limitations of measurement and modeling at such high frequencies and contemplate the future research outlook toward realizing the 6G vision.