The term cognitive computing (CC) refers to computer systems that harness multiple techniques from artificial intelligence (AI) and signal processing (SP). Situational understanding (SU) involves creating and reasoning about models of an environment and events. Coalition operations are defined by multiple partners seeking to achieve a common purpose. This paper characterises the SU problem in a coalition operations context-coalition situational understanding (CSU)-in terms of a set of problem attributes. The paper argues that CSU problems require CC system solutions involving a hybrid of AI and SP approaches. The paper outlines some of the architectural choices for CC CSU systems.