Objective: To present an overview on the current state of the art concerning metrics-based quality evaluation of software components and component assemblies. Method: Comparison of several approaches available in the literature, using a framework comprising several aspects, such as scope, intent, definition technique, and maturity. Results: The identification of common shortcomings of current approaches, such as ambiguity in definition, lack of adequacy of the specifying formalisms and insufficient validation of current quality models and metrics for software components. Conclusions: Quality evaluation of components and component-based infrastructures presents new challenges to the Experimental Software Engineering community.