The Moon is the only celestial body that human beings have visited. The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions. In the 21st century, new lunar missions including the construction of the lunar space station, the permanent lunar base, and the Earth-Moon transportation network have been proposed, requiring low-cost, expansive launch windows and a fixed arrival epoch for any launch date within the launch window. The low-energy and low-thrust transfers are promising strategies to satisfy the demands. This review provides a detailed landscape of Earth-Moon transfer trajectory design processes, from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods. Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp the basic overview of the current Earth-Moon transfer orbit design methods and a deep academic background is unnecessary for the context understanding.