There is a growing tendency to assess resilience and sustainability of critical infrastructures (CI), given the significant increment in high-impact natural hazard events affecting socio-economic welfare. Historically, these assessments have been conducted separately due to the independent evolution of each concept. However, recent contributions tend to integrate them. This paper provides a state-of-the-art review of integrated assessments for resilience and sustainability in CI, examining concepts, indicators, frameworks, and methodologies. Additionally, a Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis was performed to gain further insights into the prospects of integrated assessments. Following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology, eligibility criteria were established, leading to the selection of twelve studies. These works were compared based on five dimensions (economic, environmental, social, technical, and governance) to highlight the differences in the indicators used. While all studies considered the social, environmental, and economic dimensions, some did not further analyze sufficient indicators to evaluate environmental and social effects, with governance often neglected. This study emphasizes the relevance of establishing common metrics for a convergent frame for the resilience and sustainability assessment. The findings presented suggest that integrated assessments lead to a more strategic use of resources toward more resilient CI.