More than 40% of the world’s population still relies on traditional biomass for their cooking needs. A shift to advanced cookstoves can bring significant health and environmental benefits, but only with near exclusive use which requires significant changes in users’ behaviours. Since the emergence of the Global Alliance for Clean Cookstoves (now the Clean Cooking Alliance) in 2011, more attention has been directed to consumer and demand side factors in clean cookstove adoption and efforts to better understand individuals’ behaviours, household dynamics and decision making around the adoption of clean cookstoves and fuels have increased. This paper presents a review of the academic literature (2013–2020) and aims to identify the most successful interventions of behaviour change techniques in the adoption of improved cookstoves as well as the most common barriers to success cited in the literature. The study sourced 40 peer reviewed published academic papers from spring 2013 to summer 2020, and identified the following most commonly used behaviour change techniques in the adoption of improved cookstoves: Shaping Knowledge (n = 19), Reward & Threat (n = 13), Social Support (n = 9), Comparisons (n = 4), Identity/Self-Belief (n = 4), Regulation (n = 0), Change in the Physical Environment (n = 2), Goals & Planning (n = 6). Based on these results, we present gaps in the literature and provide policy recommendations to promote the adoption and continued use of improved cookstoves.