AI integration is revolutionizing the landscape of HPC simulations, enhancing the importance, use, and performance of AI-driven HPC workflows. This paper surveys the diverse and rapidly evolving field of AI-driven HPC and provides a common conceptual basis for understanding AI-driven HPC workflows. Specifically, we use insights from different modes of coupling AI into HPC workflows to propose six execution motifs most commonly found in scientific applications. The proposed set of execution motifs is by definition incomplete and evolving. However, they allow us to analyze the primary performance challenges underpinning AI-driven HPC workflows. We close with a listing of open challenges, research issues, and suggested areas of investigation including the the need for specific benchmarks that will help evaluate and improve the execution of AI-driven HPC workflows.