With outstanding features, Machine Learning (ML) has been the backbone of numerous applications in wireless networks. However, the conventional ML approaches have been facing many challenges in practical implementation, such as the lack of labeled data, the constantly changing wireless environments, the long training process, and the limited capacity of wireless devices. These challenges, if not addressed, will impede the effectiveness and applicability of ML in future wireless networks. To address these problems, Transfer Learning (TL) has recently emerged to be a very promising solution. The core idea of TL is to leverage and synthesize distilled knowledge from similar tasks as well as from valuable experiences accumulated from the past to facilitate the learning of new problems. Doing so, TL techniques can reduce the dependence on labeled data, improve the learning speed, and enhance the ML methods' robustness to different wireless environments. This article aims to provide a comprehensive survey on applications of TL in wireless networks. Particularly, we first provide an overview of TL including formal definitions, classification, and various types of TL techniques. We then discuss diverse TL approaches proposed to address emerging issues in wireless networks. The issues include spectrum management, localization, signal recognition, security, human activity recognition and caching, which are all important to next-generation networks such as 5G and beyond. Finally, we highlight important challenges, open issues, and future research directions of TL in future wireless networks.