<p>Fog and edge computing bring computational resources closer to end users, which is necessary for the rapid growth of applications that are latency-sensitive and bandwidth-intensive. The service placement is a significant issue since optimizing it depends on several dynamic variables, including the network’s topology, heterogeneity, and available resources. These issues are challenging due to their high level of complexity, which is why Artificial Intelligence (AI)-driven solutions are so appealing. In this article, we present a systematic literature review for service placement strategies in fog and edge computing environments that use heuristic optimization, reinforcement learning, and deep learning for optimization. Further, we propose a comprehensive taxonomy to thoroughly categorize and evaluate current methods according to performance indicators like energy usage, latency reduction, network utilization, quality of service, and general workload flexibility. Additionally, this work establishes a correlation between metric priority and methodological trends throughout the research period. One of our main contributions is the methodical categorization and critical evaluation of heuristic approaches, which shows how they are changing in their ability to balance computational efficiency and solution quality, especially in dynamic, large-scale edge contexts and multi-objective optimization. This paper acts as a guide for professionals and practitioners in the rapidly evolving field of AI-based service placement solutions and highlights new directions to help define future research topics.</p>