The ever-growing demand for increased data rates, reduced latency, and more reliable connectivity has driven the emergence of the fifth-generation (5G) wireless communication network, necessitating a significant shift in our approach to channel modeling. To achieve these ambitious goals, channel models must adopt various key enabling technologies, such as massive multiple input multiple outputs (MIMO), beamforming, and mobile edge computing, for various scenario-based applications, and adhere to developed channel standards. Our work comprehensively reviews various wireless channel models, emphasizing their applications and challenges. A concise overview of channel models for 5G and beyond provides important information about various channel modeling approaches, their standards, and protocols that are significant to their development for diverse applications in real-world scenarios. A complete list of standard channel models used in the industry, such as the third-generation partnership project, METIS, QuaDRiGa, and mmMAGIC, will help researchers and application developers understand the needs of different fields to achieve their Key Performance Indicators (KPIs). The paper also highlights important features of each channel model with a comparison of important channel characteristics and identified channel modeling issues reported in the current literature. This paper also explores the connections between channel models and other revolutionary (cutting-edge) technologies, including the use of soft computing tools (machine learning), data handling tools (cloud computing and big data analytics), and massive MIMO for use-case realization. The paper concludes that there is a need for further advancements in channel modeling to meet the requirements of the next generation by effectively addressing the challenges of the current generation. Extreme scenario channel models such as aeronautics, UAVs, deep space exploration, and massive MIMO channels require the inclusion of advanced machine learning techniques for improved performance.