This paper presents a systematic review of mapping and scheduling strategies within the High-Performance Computing (HPC) compute continuum, with a particular emphasis on heterogeneous systems. It introduces a prototype workflow to establish foundational concepts in workload characterization and resource allocation. Building on this, a thorough analysis of 66 selected research papers - spanning the period from 2017 to 2024 - is conducted, evaluating contemporary tools and techniques used for workload mapping and scheduling. The review highlights that conventional Job Shop scheduling formulations often lack the expressiveness required to model the complexity of modern HPC data centers effectively. It also reaffirms the classification of HPC scheduling problems as NP-hard, due to their combinatorial nature and the diversity of system and workload constraints. The analysis reveals a prevailing reliance on heuristic and meta-heuristic strategies, including nature-inspired, evolutionary, sorting, and search algorithms. To bridge the observed gaps, the study advocates for hybrid optimization approaches that strategically integrate heuristics, meta-heuristics, machine learning, and emerging quantum computing techniques. Such integration, when tailored to specific problem domains, holds promise for significantly improving the scalability, efficiency, and adaptability of workload optimization in heterogeneous HPC environments.