Mobile edge clouds (MECs) bring the benefits of the cloud closer to the user, by installing small cloud infrastructures at the network edge. This enables a new breed of real-time applications, such as instantaneous object recognition and safety assistance in intelligent transportation systems, that require very low latency. One key issue that comes with proximity is how to ensure that users always receive good performance as they move across different locations. Migrating services between MECs is seen as the means to achieve this. This article presents a layered framework for migrating active service applications that are encapsulated either in virtual machines (VMs) or containers. This layering approach allows a substantial reduction in service downtime. The framework is easy to implement using readily available technologies, and one of its key advantages is that it supports containers, which is a promising emerging technology that offers tangible benefits over VMs. The migration performance of various real applications is evaluated by experiments under the presented framework. Insights drawn from the experimentation results are discussed.