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Explosion containment vessels (ECVs), which can be generally classified into three categories, i.e., multiple use ECVs and one-time use ECVs, single-layered ECVs and multi-layered ECVs, metallic ECVs and composite ECVs according to the usage, structural form and the bearing unit, respectively, are widely used to completely contain the effects of explosions. There are fundamental differences between statically-loaded pressure vessels and ECVs that operate under extremely fast loading conditions. Conventional pressure design codes, such as ASME Section VIII, EN13445 etc., can not be directly used to design ECVs. So far, a lot of investigations have been conducted to establish design method for ECVs. Several predominant effects involved in the design of ECVs such as scale effect, failure mode and failure criteria are extensively reviewed. For multiple use single-layered metallic ECVs, dynamic load factor method and AWE method are discussed. For multiple use composite ECVs, a minimum strain criteria based on explosion experiments is examined. For one-time use ECVs, a strain limit method proposed by LANL and a maximum strain criteria obtained by Russia are discussed for metallic vessel and composite vessel, respectively. Some improvements and possible future work in developing design criterion for ECVs are recommended as a conclusion.