The demand for distributed applications has significantly increased over the past decade, with improvements in machine learning techniques fueling this growth. These applications predominantly utilize Cloud data centers for high-performance computing and Fog and Edge devices for low-latency communication for small-size machine learning model training and inference. The challenge of executing applications with different requirements on heterogeneous devices requires effective methods for solving NP-hard resource allocation and application scheduling problems. The state-of-the-art techniques primarily investigate conflicting objectives, such as the completion time, energy consumption, and economic cost of application execution on the Cloud, Fog, and Edge computing infrastructure. Therefore, in this work, we review these research works considering their objectives, methods, and evaluation tools. Based on the review, we provide a discussion on the scheduling methods in the Computing Continuum.

7 pages, 3 figures, 3 tables