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Few-shot learning (FSL) has emerged as an effective learning method and shows great potential. Despite the recent creative works in tackling FSL tasks, learning valid information rapidly from just a few or even zero samples still remains a serious challenge. In this context, we extensively investigated 200+ latest papers on FSL published in the past three years, aiming to present a timely and comprehensive overview of the most recent advances in FSL along with impartial comparisons of the strengths and weaknesses of the existing works. For the sake of avoiding conceptual confusion, we first elaborate and compare a set of similar concepts including few-shot learning, transfer learning, and meta-learning. Furthermore, we propose a novel taxonomy to classify the existing work according to the level of abstraction of knowledge in accordance with the challenges of FSL. To enrich this survey, in each subsection we provide in-depth analysis and insightful discussion about recent advances on these topics. Moreover, taking computer vision as an example, we highlight the important application of FSL, covering various research hotspots. Finally, we conclude the survey with unique insights into the technology evolution trends together with potential future research opportunities in the hope of providing guidance to follow-up research.