Industrial equipment located in coastal areas is becoming more exposed to the risk of natural disasters due to increased frequencies and severities, as demonstrated on several occasions, such as the 2011 Great East Japan Earthquake, emphasizing the need to incorporate multi-hazard perspectives in risk-informed decision-making. Among these, earthquake-induced tsunamis present a complex challenge as they involve consecutive, interrelated hazards that can greatly enhance damage. This paper presents a state-of-the-art review of methodologies for multi-hazard risk analysis of industrial equipment subjected to seismic-related events, with a particular focus on the combined effects of earthquakes and subsequent tsunamis. While seismic vulnerability assessment is a well-established field, tsunami vulnerability-especially in the context of cascading hazards-remains less explored and lacks standardized evaluation frameworks. We examine current approaches used to model hazard interactions, assess vulnerability and fragility, and estimate risk under multi-hazard conditions. Special attention is directed toward fragility curves for tsunamis and risk loads, to assess whether the impact of prior seismic damage on equipment performance has been analyzed, and if the integration of time-dependent effects has been implemented. This review aims to survey existing literature, identify challenges and prospects, and address gaps to more effectively capture the complexities of natural hazard interactions affecting critical industrial infrastructure.