  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.
