Research on energy poverty has advanced significantly over the past three decades, yet this progress has occurred along largely separate tracks. The Capability Approach (CA) examines how energy shapes household wellbeing, while the energy justice framework examines the equitable distribution, governance, and recognition of energy systems, with limited dialogue between the two. Measurement approaches have likewise evolved in parallel, moving from access and expenditure-based indicators to multidimensional and more recently, required consumption-based frameworks, yet no existing approach connects household-level deprivation to the structural and institutional conditions that produce it. This fragmentation leaves a critical gap: without an integrated theoretical and measurement approach, it remains unclear why energy poverty persists in rural South Africa despite decades of electrification. This paper addresses that gap through an integrative review that examines the conceptual evolution of energy poverty, evaluates existing measurement approaches, and synthesizes the CA, energy justice, and emerging evidence on social capital into a single framework. The review conceptualizes energy poverty as a dynamic process of household energy vulnerability, linking structural conditions, energy system performance, household characteristics, capability conversion, and welfare outcomes, offering a stronger foundation for measurement, interdisciplinary research, and policy aimed at household resilience.