Intelligent Reflecting Surface (IRS) is envisioned to be a technical enabler for the sixth-generation (6G) wireless system. Its potential lies in delivering high performance while maintaining both power efficiency and cost-effectiveness. Previous studies have primarily focused on point-to-point IRS communications involving a single user. Nevertheless, a practical system must serve multiple users simultaneously. The unique characteristics of IRS, such as non-frequency-selective reflection and the necessity for joint active/passive beamforming, create obstacles to the use of conventional multiple access (MA) techniques. This motivates us to review various MA techniques to make clear their functionalities in the presence of IRS. Through this paper, our aim is to provide researchers with a comprehensive understanding of challenges and available solutions, offering insights to foster their design of efficient multiple access for IRS-aided systems.