The field of wireless communication networks has witnessed a dramatic change over the last decade due to sophisticated technologies deployed to satisfy various demands peculiar to different data-intensive wireless applications. Consequently, this has led to the aggressive use of the available propagation channels to fulfill the minimum quality of service (QoS) requirement. A major barometer used to gauge the performance of a wireless communication system is the spectral efficiency (SE) of its communication channels. A key technology used to improve SE substantially is the multiple input multiple output (MIMO) technique. This article presents a detailed survey of MIMO channel models in wireless communication systems. First, we present the general MIMO channel model and identified three major MIMO channel models, viz., the physical, analytical, and standardized models. The physical models describe the MIMO channel using physical parameters. The analytical models show the statistical features of the MIMO channel with respect to the measured data. The standardized models provide a unified framework for modern radio propagation architecture, advanced signal processing, and cutting-edge multiple access techniques. Additionally, we examined the strengths and limitations of the existing channel models and discussed model design, development, parameterization, implementation, and validation. Finally, we present the recent 3GPP-based 3D channel model, the transitioning from 2D to 3D channel modeling, discuss open issues, and highlight vital lessons learned for future research exploration in MIMO communication systems.