As global energy concerns escalate, there is a growing need for effective strategies to promote sustainable energy practices among individuals and communities. Gamification, the integration of game-design elements in non-game contexts, emerges as a promising tool to enhance user engagement and foster sustainable behaviour in energy management. In this review, we examine the theoretical aspects of gamification and its application in energy management in users' households, highlighting its potential to transform repetitive or even monotonous tasks into engaging activities, focusing on studies that measure a long-term effect. We delve into various gamified elements adopted in long-term studies, such as feedback, social interactions, point systems, leader boards, narrative-driven challenges, etc., to understand their effect on user motivation and behavioural changes. From our set of studies, we found out that strong social game elements contribute the most to the long-term behaviour change of energy usage. One more condition of behaviour change is strong positive user satisfaction: the game should be engaging. We highlight the possible limitations of gamification in an energy management situation, a strong need for better practices of design and evaluation, and innovative approaches (such as DSM; Demand Side Management) in gamification for long-term engagement in household energy management.