Recently, broadband maritime communication has attracted much attention due to the rapid development of blue economy. In addition to the conventional MF/HF/VHF bands, there has been increasing interests in the utilization of higher frequency bands to provide broadband data service to the sea area. To design efficient maritime communication systems, the first and a fundamental requirement is to develop a framework to understand the wireless channels. In an integrated air-ground-sea communications network, there are two major type of channels to be investigated, namely the air-to-sea channel (e.g., for communication links from the aircraft-based base stations or relays) and the near-sea-surface channel (for land-to-ship/ship-to-land or ship-to-ship communications). Due to the unique features of the maritime propagation environment such as sparse scattering, sea wave movement, and the ducting effect over the sea surface, the modeling of these maritime channel links differs from conventional terrestrial wireless channels in many aspects and, consequently, will result in significant impact on the transceiver design. In this survey, we highlight the most notable differences from the modeling perspective as well as the channel characteristics for the air-to-sea and near-sea-surface channel links, with more focus on the latter. After a thorough review of existing modeling approaches and measurement campaigns, we conclude that the sparse and the location-dependent properties constitute the most important and distinctive characteristics of the maritime wireless channels. As such, we further remark on the challenges and research topics for future development of maritime communications.