This article focuses on the near-field effect in terahertz (THz) communications and sensing systems. By equipping with extremely large-scale antenna arrays (ELAAs), the near-field region in THz systems can be possibly extended to hundreds of meters in proximity to THz transceivers, which necessitates the consideration of near-field effect in the THz band both for the communications and sensing. We first review the main characteristics of the near-field region in the THz bands. The signal propagation in the near-field region is characterized by spherical waves rather than planar waves in the far-field region. This distinction introduces a new distance dimension to the communication and sensing channels, which brings new opportunities and challenges for both THz communications and sensing. More particularly, 1) For THz communications, the near-field effect enables a new mechanism for beamforming, namely, beamfocusing, in the focusing region. Furthermore, in THz multiple-input and multiple-output (MIMO) systems, the near-field effect can be exploited to combat the multiplexing gain degradation caused by the sparse THz channels. To address the near-field beam split effect caused by the conventional frequency-independent hybrid beamforming architecture in THz wideband communications, we propose a pair of wideband beamforming optimization approaches by a new hybrid beamforming architecture based on true-time-delayers (TTDs). 2) For THz sensing, joint angle and distance sensing can be achieved in the near-field region. Additionally, the near-field beam split becomes a beneficial effect for enhancing the sensing performance by focusing on multiple possible target locations rather than a drawback encountered in communications. Finally, several topics for future research are discussed.