The internet of things (IoT) is essential for the implementation of applications and services that require the ability to sense the surrounding environment through sensors and modify it through actuators. However, IoT devices usually have limited computing capabilities and hence are not always sufficient to directly host resource-intensive services. Fog computing, which extends and complements the cloud, can support the IoT with computing resources and services that are deployed close to where data are sensed and actions need to be performed. Virtualisation is an essential feature in the cloud as in the fog, and containers have been recently getting much popularity to encapsulate fog services. Besides, container migration among fog nodes may enable several emerging use cases in different IoT domains (e.g., smart transportation, smart industry). In this paper, we first report container migration use cases in the fog and discuss containerisation. We then provide a comprehensive overview of the state-of-the-art migration techniques for containers, i.e., cold, pre-copy, post-copy, and hybrid migrations. The main contribution of this work is the extensive performance evaluation of these techniques that we conducted over a real fog computing testbed. The obtained results shed light on container migration within fog computing environments by clarifying, in general, which migration technique might be the most appropriate under certain network and service conditions.