The increasing demand for intelligent services and privacy protection of mobile and Internet of Things (IoT) devices motivates the wide application of Federated Edge Learning (FEL), in which devices collaboratively train on-device Machine Learning (ML) models without sharing their private data. \textcolor{black}{Limited by device hardware, diverse user behaviors and network infrastructure, the algorithm design of FEL faces challenges related to resources, personalization and network environments}, and Knowledge Distillation (KD) has been leveraged as an important technique to tackle the above challenges in FEL. In this paper, we investigate the works that KD applies to FEL, discuss the limitations and open problems of existing KD-based FEL approaches, and provide guidance for their real deployment.