Group moving pattern is an essential problem in spatio-temporal trajectory pattern mining which is used to get group moving rules, group moving trend and group events. The problems and challenges of group moving pattern modeling and mining are analyzed. Group moving patterns are classified as having leaders moving pattern, company moving pattern, mutant moving pattern, popular moving pattern, aggregation moving pattern, and divergence moving pattern. The difference and connection between different group moving patterns and the idea of algorithms for mining group moving patterns are introduced.