Low-income households face long-standing challenges of energy insecurity and inequality (EII). During extreme events (e.g., disasters and pandemics) these challenges are especially severe for vulnerable populations reliant on energy for health, education, and well-being. However, many EII studies rarely incorporate the micro- and macro-perspectives of resilience and reliability of energy and internet infrastructure and social-psychological factors. To remedy this gap, we first address the impacts of extreme events on EII among vulnerable populations. Second, we evaluate the driving factors of EII and how they change during disasters. Third, we situate these inequalities within broader energy systems and pinpoint the importance of equitable infrastructure systems by examining infrastructure reliability and resilience and the role of renewable technologies. Then, we consider the factors influencing energy consumption, such as energy practices, socio-psychological factors, and internet access. Finally, we propose interdisciplinary research methods to study these issues during extreme events and provide recommendations.