Owing to its unique spectral characteristics, the terahertz(THz) frequency band demonstrates broad application prospects in high-resolution automotive radar, short-range high-data-rate communications, interstellar communications, and biomedical imaging. As a critical transmitting and receiving component in terahertz systems, antennas directly influence the system operating range and coverage. Current research on terahertz array antennas primarily focuses on enhancing gain and efficiency, broadening bandwidth, and beam scanning. This paper reviews the current development status and challenges of terahertz array antennas in terms of their key performance metrics, discusses recent advances in wideband high-gain antennas, beam-steering antennas, large-scale MIMO arrays, and on-chip integrated antennas, and presents an antenna array design methodology based on the Maximum Power Transfer Efficiency(MMPTE) method along with its unique advantages in terahertz antenna design, aiming to provide insights for the further advancement of terahertz array antennas.