Research on lower limb exoskeleton (LLE) for rehabilitation have developed rapidly to meet the need of the population with neurologic injuries. LLEs for rehabilitation include therapeutic LLEs that aim to restore walking ability for patients, and assistive LLEs that offer support on activities in daily life. A substantial part of them can serve both purposes. However, these devices are yet to reach the final goal of performing human-machine joint movement agilely and smartly. Control strategy plays an important role in achieving their designed goal. At present, control strategies face three major challenges: how to detect human intention, how to do motion control with given intentions, and how to optimize control parameters to suit different individuals. As a contribution, this paper offers an overview on the state-of-the-art control strategies for rehabilitation LLEs by classifying them into eight categories, each of which is presented with a technical summary and tabulated information of representative papers. Moreover, current approaches addressing the three challenges are discussed in a macroscopic perspective. Finally, it has been explored which requirements the future control strategies should meet for maximizing the performance of rehabilitation LLEs.