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Transfer learning (TL) utilizes data or knowledge from one or more source domains to facilitate the learning in a target domain. It is particularly useful when the target domain has very few or no labeled data, due to annotation expense, privacy concerns, etc. Unfortunately, the effectiveness of TL is not always guaranteed. Negative transfer (NT), i.e., leveraging source domain data/knowledge undesirably reduces the learning performance in the target domain, has been a long-standing and challenging problem in TL. Various approaches have been proposed in the literature to handle it. However, there does not exist a systematic survey on the formulation of NT, the factors leading to NT, and the algorithms that mitigate NT. This paper fills this gap, by first introducing the definition of NT and its factors, then reviewing about fifty representative approaches for overcoming NT, according to four categories: secure transfer, domain similarity estimation, distant transfer, and NT mitigation. NT in related fields, e.g., multi-task learning, lifelong learning, and adversarial attacks, are also discussed.