This is a survey of various research papers on the topic of Model-Agnostic Meta-Learning (MAML) and represents a systematic knowledge of its principles, versions, and implementations. In order to arrange the existing disjointed literature, the research houses a four-part taxonomy including: (i) fundamental principles of MAML and two-level optimization, (ii) significant algorithmic variants, including Reptile, ProtoNets, first-order MAML, Agnostic-SAM, and AMFS, (iii) domain-specific applications, including robotics, vision, NLP, reinforcement learning, and healthcare, and (iv) open issues, including scalability, computational cost, and training stability. The review themes the recent progress in traditional activities, such as gradient-efficient updates, geometry-adaptive preconditioning, and sparse or sharpness-conscious optimization, have been synthesized to analyze the ways in which current versions reduce the high computational cost of MAML and are less sensitive to hyperparameters. Average results suggest that an MAML typically matches or exceeds alternatives in few-shot learning settings, whereas even simpler metric-based models can do well in low-variance environments. This survey offers a summary of the trade-offs between generalization and efficiency that have continually been persistent in spite of proposed theoretical foundations, empirical findings, and implementation recommendations to create scalable and robust meta-learning approaches that can be used in practice.