Monitoring progress towards the Sustainable Development Goals by 2030 requires the global community to disaggregate targets along socio-economic lines, but little has been published critically analyzing the appropriateness of wealth indices to measure socioeconomic status in low- and middle-income countries. This critical interpretive synthesis analyzes the appropriateness of wealth indices for measuring social health inequalities and provides an overview of alternative methods to calculate wealth indices using data captured in standardized household surveys. Our aggregation of all published associations of wealth indices indicates a mean Spearman’s rho of 0.42 and 0.55 with income and consumption, respectively. Context-specific factors such as country development level may affect the concordance of health and educational outcomes with wealth indices and urban–rural disparities can be more pronounced using wealth indices compared to income or consumption. Synthesis of potential future uses of wealth indices suggests that it is possible to quantify wealth inequality using household assets, that the index can be used to study SES across national boundaries, and that technological innovations may soon change how asset wealth is measured. Finally, a review of alternative approaches to constructing household asset indices suggests lack of evidence of superiority for count measures, item response theory, and Mokken scale analysis, but points to evidence-based advantages for multiple correspondence analysis, polychoric PCA and predicted income. In sum, wealth indices are an equally valid, but distinct measure of household SES from income and consumption measures, and more research is needed into their potential applications for international health inequality measurement.