Liner shipping plays a major role for freight transportation and international seaborne trade. The economic development of different countries is significantly dependent on the movement of a containerized cargo. One of the most challenging decision problems, tackled by liner shipping companies, is the design of vessel schedules. At the vessel scheduling stage, the liner shipping company aims to determine vessel sailing speeds at voyage legs of a given liner shipping route, port times, vessel handling rates at ports, the minimum number of vessels required in order to provide the agreed service frequency at ports, and other factors. Considering the existing pollution levels, the environmental impacts of liner shipping have to be captured in the vessel scheduling models as well. This study conducts a comprehensive survey of the existing research on vessel scheduling in liner shipping. The collected vessel scheduling studies are classified into different categories, including general vessel scheduling, uncertainty in liner shipping operations, collaborative agreements, vessel schedule recovery, and green liner shipping. Based on a detailed analysis of the collected literature, findings are discussed, and limitations in the state-of-the-art are identified for each category of studies. The study concludes with a number of future research opportunities, taking into account the recent developments and trends in liner shipping.