Materials scientists and engineers have been trying to create porous metals and metal foams for many years. Naturally occurring porous materials such as bone, coral, cork, balsa wood, etc., are responsible for initiating research in the area of producing porous metals and metal foams. Metal foam is a cellular structure made up of a solid metal-containing a large volume fraction of gas-filled pores. These pores can either be sealed (closed-cell foam), or they can be an interconnected network (open-cell foam). The closed-cell foam is referred to as metal foams, while the open-cell foam is referred to simply as porous metal. Some of the key properties of the metal foam are, ultra-light material (75–95% of the volume consists of void spaces), very high porosity, and high compression strengths combined with good energy absorption characteristics. This paper provides a comprehensive review of mechanical characterizations of closed-cell aluminum metal foams (CCAFs) or porous aluminum alloys, the trends in their mechanical behavior specifically their compressive performance. The significant factors influencing this behavior are intricately studied in light of the available literature. The aim of this work is to facilitate a channelized development over the past few decades in the field of mechanical behavior of CCAF that may be of help to the researchers, academicians, and industries for the critical understanding of the failure criteria and mechanical properties of closed-cell aluminum metal foams.