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Semantic communication (SemCom) aims to convey the meaning behind a transmitted message by transmitting only semantically-relevant information. This semantic-centric design helps to minimize power usage, bandwidth consumption, and transmission delay. SemCom and goal-oriented SemCom (or effectiveness-level SemCom) are therefore promising enablers of 6G and developing rapidly. Despite the surge in their swift development, the design, analysis, optimization, and realization of robust and intelligent SemCom as well as goal-oriented SemCom are fraught with many fundamental challenges. One of the challenges is that the lack of unified/universal metrics of SemCom and goal-oriented SemCom can stifle research progress on their respective algorithmic, theoretical, and implementation frontiers. Consequently, this survey paper documents the existing metrics– scattered in many references– of wireless SemCom, optical SemCom, quantum SemCom, and goal-oriented wireless SemCom. By doing so, this paper aims to inspire the design, analysis, and optimization of a wide variety of SemCom and goal-oriented SemCom systems. This article also stimulates the development of unified/universal performance assessment metrics of SemCom and goal-oriented SemCom, as the existing metrics are purely statistical and hardly applicable to reasoning-type tasks that constitute the heart of 6G and beyond.