As radio access technologies, processing speeds, and multimode interfaces of low-powered portable devices continue to advance, the future of wireless communication is envisioned to offer pervasive network coverage, high data rates, and a wide spectrum of services while maintaining high mobility. High data rates, wide range of services, huge connectivity, capacity, and good geographic coverage are being provided by the ultra-dense deployment of small base stations (BSs) in heterogeneous wireless networks (HWN). But dense deployment of small BSs, high mobility, network heterogeneity, imbalanced traffic, and dynamic user preferences lead to frequent handover. Network overhead, excessive energy consumption, and a decrease in service quality and user satisfaction can be due to frequent handover. So, handover management is one of the crucial challenges in the implementation of 5G and beyond in HWNs for ensuring seamless connectivity, energy efficiency, and the required quality of services and experiences. The effectiveness of handover decisions in HWNs relies on the implementation of a suitable network selection mechanism. Multi-attribute decision-making (MADM) is being used to model and analyze appropriate network selection complexities by considering a broad spectrum of intricate and conflicting decision criteria for efficient handover decisions in HWN. This article extensively explores, compares, and analyzes vital MADM techniques utilized for modeling appropriate network selection strategies in terms of algorithmic strategies, cardinality, types and significance of decision attributes, and network utilities. This article also examines, analyzes, and recognizes the recent mobility management challenges and trends in utilizing MADM strategies to tackle network selection issues in high-speed HWNs. © 2024 The Author(s)