The problem of optimizing the execution of Artificial Intelligence (AI) and Deep Learning (DL) applications in the Computing Continuum gained remarkable popularity in recent years, due to both the widespread adoption of AI in real-life scenarios and the challenging environment introduced by a distributed Edge-to-Cloud paradigm. We tackled the resource selection, scheduling and placement problem both from a design-time and runtime perspective, considering, on one hand, AI inference applications characterized by complex workflows with multiple heterogeneous components and, on the other hand, resource-demanding DL training jobs executed on public or private GPU-accelerated clusters.