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Human intelligence is characterized by our ability to absorb and apply knowledge from the world around us, especially in rapidly acquiring new concepts from minimal examples, underpinned by prior knowledge. Few-shot learning (FSL) aims to mimic this capacity by enabling significant generalizations and transferability. However, traditional FSL frameworks often rely on assumptions of clean, complete, and static data, conditions that are seldom met in real-world environments. Such assumptions falter in the inherently uncertain, incomplete, and dynamic contexts of the open world. This paper presents a comprehensive review of recent advancements designed to adapt FSL for use in open-world settings. We categorize existing methods into three distinct types of open-world few-shot learning: those involving varying instances, varying classes, and varying distributions. Each category is discussed in terms of its specific challenges and methods, as well as its strengths and weaknesses. We standardize experimental settings and metric benchmarks across scenarios, and provide a comparative analysis of the performance of various methods. In conclusion, we outline potential future research directions for this evolving field. It is our hope that this review will catalyze further development of effective solutions to these complex challenges, thereby advancing the field of artificial intelligence.