The interdependence of container shipping operations (CSOs) creates a hotbed of multiple operational risks. Risk analysis and assessment (RAA) is, therefore, a growing research focus on container shipping policy and management. Currently, it is challenging to grasp a state-of-the-art understanding of the field due to the fragmentation of the central concepts and overlapping taxonomies. This critical review paper clearly indicates this fragmentation by an overarching framework to cover both CSO and RAA aspects. The results revealed the attention toward ports and container shipping companies as the primary subjects of research; and Asia-Pacific and Europe as the fruitful regions of empirical studies. Thirty-five typical information, physical, and financial risks were identified in various CSOs. Regarding the CSO aspect, besides more empirical applications of RAA models, approaches and methods to support the collaborative mitigation and prevention efforts are considered critical tasks of the field, especially in the upcoming era of digitalization in container shipping. Regarding the RAA aspect, the establishment of a common framework that acknowledges uncertainty as a core component of risk is necessary to support the CSO aspect in dealing with emerging issues.