The Computing Continuum (CC) integrates different layers of processing infrastructure, from Edge to Cloud, to optimize service quality through ubiquitous and reliable computation. Compared to central architectures, however, heterogeneous and dynamic infrastructure increases the complexity for service orchestration. To guide research, this article first summarizes structural problems of the CC, and then, envisions an ideal solution for autonomous service orchestration across the CC. As one instantiation, we show how Active Inference, a concept from neuroscience, can support self-organizing services in continuously interpreting their environment to optimize service quality. Still, we conclude that no existing solution achieves our vision, but that research on service orchestration faces several structural challenges. Most notably: provide standardized simulation and evaluation environments for comparing the performance of orchestration mechanisms. Together, the challenges outline a research roadmap toward resilient and scalable service orchestration in the CC.