This study explores the personalization of gamification in educational contexts, particularly adaptive approaches to meet diverse learner needs. The study examines terminologies and offer definitions for adaptive, tailored, personalized, and customized gamification. Personalization serves as an umbrella term covering any changes in the process. Customization is the changes performed by the user/learner; tailored gamification involves adjustments made at the beginning and adaptive gamification involves system-driven changes as things progress. The analysis of adaptive gamification studies is structured around adaptation criteria, adaptation process, adaptation data, and adaptive intervention. Adaptation criteria includes player types, personality models, learning styles, and hybrid profiles. Adaptation process includes user-controlled and system-controlled adaptation. User-controlled adaptation refers to customization; system-controlled adaptation is examined under static adaptation, dynamic adaptation, and combination of these two. Adaptation data is categorized under explicit and implicit information collection. Lastly, recommendations, and adjusting game elements and mechanics are discussed under adaptation intervention. The review highlights the commonly used player typologies, including Bartle, Hexad, and BrainHex, and personality models such as Big Five and Myers-Briggs Type Indicator. The review identifies limitations in current frameworks, stressing the importance of standardized models and guidelines to implement adaptive gamification and incorporating gamification analytics to sustain adaptation and automation.