Artificial Intelligence Generated Content (AIGC) refers to the automatic generation of various types of content—such as text, images, audio, and video—using artificial intelligence techniques. In recent years, AIGC has been widely applied across domains including software development, education, advertising, online customer service and beyond, significantly transforming the content creation paradigm and reshaping human–computer interaction. With the increasing computational capabilities of mobile devices, the proliferation of intelligent computing at the network edge, and growing user demands for low-latency, bandwidth-efficient, and privacy-preserving AIGC services, Mobile Edge Networks (MENs) have emerged as a promising infrastructure for delivering AIGC services efficiently and responsively. This survey provides an overview of the opportunities and challenges associated with deploying AIGC on mobile edge networks. We highlight the significance of enabling AIGC under the MENs paradigm and examine the key supporting technologies and system infrastructures—such as resource allocation, task offloading, and edge caching—that empower users to access AIGC services seamlessly at the edge. Finally, we outline future research directions and open issues in mobile AIGC networks to guide further investigation in this emerging field.