To tackle the sub-optimization problem of the conventional block structure communication systems, recently, a novel concept named end-to-end communication system that can optimize the whole system jointly has been proposed. A channel autoencoder (AE) is one of the methods, which regards the wireless communication system as an AE along with a channel model. In this article, we present a comprehensive overview of the recent advancements of channel AEs, whose practicability mainly depends on the robustness of the impairments in actual channels. Among existing works, assuming the imperfect channel models before training or constructing a communication system without channel models are both viable methods to deal with channel impairments. Therefore, we divide the channel AEs into two categories, model-assumed and model-free channel AEs, for each of which a universal structure is investigated, namely radio transformer network and gradient generation network, respectively. Then their performance is compared extensively, and the open research issues are discussed in the end to provide some directions for future study.