Complex metallic alloys (CMAs) are materials composed of structurally complex intermetallic phases (SCIPs). The SCIPs consist of large unit cells containing hundreds or even thousands of atoms. Well-defined atomic clusters are found in their structure, typically of icosahedral point group symmetry. In SCIPs, a long-range order is observed. Aluminum-based CMAs contain approximately 70 at.% Al. In this paper, the corrosion behavior of bulk Al-based CMAs is reviewed. The Al–TM alloys (TM = transition metal) have been sorted according to their chemical composition. The alloys tend to passivate because of high Al concentration. The Al–Cr alloys, for example, can form protective passive layers of considerable thickness in different electrolytes. In halide-containing solutions, however, the alloys are prone to pitting corrosion. The electrochemical activity of aluminum-transition metal SCIPs is primarily determined by electrode potential of the alloying element(s). Galvanic microcells form between different SCIPs which may further accelerate the localized corrosion attack. The electrochemical nobility of individual SCIPs increases with increasing concentration of noble elements. The SCIPs with electrochemically active elements tend to dissolve in contact with nobler particles. The SCIPs with noble metals are prone to selective de-alloying (de–aluminification) and their electrochemical activity may change over time as a result of de-alloying. The metal composition of the SCIPs has a primary influence on their corrosion properties. The structural complexity is secondary and becomes important when phases with similar chemical composition, but different crystal structure, come into close physical contact.