Over the past few years, the modeling of wireless channels for radio wave propagation over the sea surface has drawn the attention of many researchers. Channel models are designed and implemented for different frequencies and communication scenarios. There are models that emphasize the influence of the height of the evaporation duct in the marine environment, as well as models that deal with different frequencies (2.5, 5, and 10 GHz, etc.) or the impact of various parameters, such as antenna height. Despite the increasing literature on channel modeling for the over-the-sea marine environment, there is no comprehensive study that focuses on key concepts that need to be considered when developing a new channel model, characteristics of channel models, and comparative analysis of existing works along with their possible improvements and future applications. In this paper, channel models are discussed in relation to their operational principles and key features, and they are compared with each other in terms of major characteristics and pros and cons. Some important insights on the design and implementation of a channel model, possible applications and improvements, and challenging issues and research directions are also discussed. The main goal of this paper is to present a comparative study of over-the-sea channel models for radio wave propagation, so that it can help engineers and researchers in this field to choose or design the appropriate channel models based on their applications, classification, features, advantages, and limitations.