The rapid development of sixth-generation (6G) wireless networks requires seamless integration of communication and sensing to support ubiquitous intelligence and real-time, high-reliability applications. Integrated sensing and communication (ISAC) has emerged as a key solution for achieving this convergence, offering joint utilization of spectral, hardware, and computing resources. However, realizing high-performance ISAC remains challenging due to environmental line-of-sight (LoS) blockage, limited spatial resolution, and the inherent coverage asymmetry and resource coupling between sensing and communication. Intelligent reflecting surfaces (IRSs), featuring low-cost, energy-efficient, and programmable electromagnetic reconfiguration, provide a promising solution to overcome these limitations. This article presents a comprehensive overview of IRS-aided wireless sensing and ISAC technologies, including IRS architectures, target detection and estimation techniques, beamforming designs, and performance metrics. It further explores IRS-enabled new opportunities for more efficient performance balancing, coexistence, and networking in ISAC systems, focuses on current design bottlenecks, and outlines future research directions. This article aims to offer a unified design framework that guides the development of practical and scalable IRS-aided ISAC systems for the next-generation wireless network.