Studying effective routing strategies has become a critical issue in construction of LEO satellite networks because satellite network resources are very limited and maintenance costs are very great. Firstly, features of LEO satellite networks distinct from terrestrial networks are summed up according to their effects on routing issues. Subsequently, a survey of various routing strategies paying particular attention to these problems from aspects of topology, routing refreshment and load balancing is provided. By analyzing the characteristic of routing schemes in their various aspects, a foundation of designing more effective routing strategies to meet the needs of future applications is laid.