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Phased array antennas (PAAs) with flexible and agile wide-angle beam scanning (WABS) abilities have drawn rapidly increasing attentions in recent years. They have found significant applications in beyond fifth-generation (B5G) and sixth-generation (6G) wireless communications, satellite communications, sensing, etc., for their outstanding capability to achieve wide spatial coverage, enable critical frequency reuse, and improve the system capacity. In this review, we aim to investigate and discuss several challenges that hinder WABS for conventional PAAs, including the strong mutual coupling, narrow beamwidth of the element antenna, etc. We then review and summarize a variety of innovative techniques to overcome these challenges. Subsequently, we discuss and analyze potential research gaps of WABS PAAs for future emerging applications. This timely review fulfills the demand of a thorough and detailed investigation on WABS technologies for PAAs and provides detailed introduction and guidance for interested researchers and engineers.