Edge computing promises low-latency and high-throughput real-time processing to enable critical and life-changing future applications such as fully autonomous driving and metaverse, and is receiving wide interest from application designers, service providers and academic researchers. As for now, however, the full power of edge computing has yet been unleashed, as stakeholders face difficulty in realizing the promised services and hence investment and efforts waver. This article describes a new conceptual framework, called the application-network co-design approach, to align and direct efforts across application, computing and networking domains towards fully fledged edge computing. At a high level, we introduce current practices and efforts in edge computing, identify limitations of existing efforts, present the overarching goal and principles of the co-design approach, and discuss existing and future prerequisite technologies for implementing the approach. We illustrate the principles and process of the co-design approach with two compelling edge applications: autonomous driving and virtual/augmented reality for metaverse.