A medium access control (MAC) protocol is designed to disseminate safety messages reliably and rapidly to improve the safety and efficiency of vehicles on the road in vehicular ad-hoc networks (VANETs). VANETs, which are created by moving vehicles, have specific properties, such as high node mobility with constrained movements and quick topology changes. Hence, MAC protocols should be designed to adapt to the changing data traffic patterns due to vehicle densities in the VANET environment. The latest multi-channel MAC protocols based on IEEE 802.11p and IEEE 1609.4 standards have higher performance than that of single-channel MAC protocols in every key performance indicator. Specifically, the multi-channel MAC protocols, which adapt themselves to different vehicular traffic densities, can guarantee a bounded transmission delay of real-time safety applications and an increased throughput for non-safety applications. In this paper, we focus on the three following perspectives: First, the multi-channel MAC protocols are studied under saturated and non-saturated data traffic conditions; Second, we study the multi-dimensional Markov chains (up to three dimensions) used in the MAC protocols; and Third, the considered Markov models are compared with real-life application requirements to improve the existing analytical models and protocol designs. Finally, we summarize our findings and discuss the open issues concerning multi-channel MAC protocols for VANETs as a part of the Intelligent Transportation System.