Most recent edge and fog computing architectures aim at pushing cloud-native traits at the edge of the network, reducing latency, power consumption, and network overhead, allowing operations to be performed close to data sources. To manage these architectures in an autonomous way, systems that materialize in specific computing nodes must deploy self-* capabilities minimizing human intervention across the continuum of computing equipment. Nowadays, a systematic classification of such capabilities is missing, as well as an analysis on how those can be implemented. For a system owner in a continuum deployment, there is not a main reference publication to consult to determine what capabilities do exist and which are the sources to rely on. In this article, a literature review is conducted to analyze the self-* capabilities needed to achieve a self-* equipped nature in truly autonomous systems. The article aims to shed light on a potential uniting taxonomy in this heterogeneous field. In addition, the results provided include conclusions on why those aspects are too heterogeneously tackled, depend hugely on specific cases, and shed light on why there is not a clear reference architecture to guide on the matter of which traits to equip the nodes with.