The emergence of AMRs has altered our perspective and relationship with automation. At the heart of this transition is navigation and obstacle avoidance, both of which are important needs for deploying AMRs in a variety of scenarios. This comprehensive review looks at the latest advances in navigation and collision avoidance for AMRs, including a wide range of modern techniques and methodologies, algorithms, and technologies that aim to improve functionality. The study provides a detailed analysis of known approaches, such as rule-based approaches, potential fields, reactive navigation systems as behavior systems, and path-following algorithms, that have been developed to address the difficulty in practice. In contrast, technological advancements in machine learning, computer vision sensor fusion, and SLAM techniques, as well as edge computing, are reviewed in light of their unprecedented impact on AMR navigation. Global and local techniques are tackled using universal worldwide optics as well as national adaptations that reveal the unique characteristics of individual countries. The Data Analysis and Processing section emphasizes the importance of technologies that define AMR performance. Due to the constraints imposed by previous studies, it is clear that additional research is required to focus on closing gaps in controlled environments and using standard benchmarks; sensor heterogeneity issues; and practical implementation of theoretical aspects. In a nutshell, this review provides a map of the complex world of AMR navigation and obstacle avoidance. Its primary purpose is to contribute to the continuing debate, promote innovation, and suggest new research avenues in a fast-changing world of autonomous mobile robotics that breaks down traditional deployment constraints.