In order to build highly reliable composite service via Service Oriented Architecture (SOA) in the Mobile Fog Computing environment, various fault tolerance strategies have been widely studied and got notable achievements. In this paper, we provide a comprehensive overview of key fault tolerance strategies. Firstly, fault tolerance strategies are categorized into static and dynamic fault tolerance according to the phase of their adoption. Secondly, we review various static fault tolerance strategies. Then, dynamic fault tolerance implementation mechanisms are analyzed. Finally, main challenges confronted by fault tolerance for composite service are reviewed.