This paper introduces the responsibilities assignment problem (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> P) and discusses existing methodologies by theory and examples. The R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> P can be understood as the evaluation and determination of the power quality disturbances and of the power quality conditions detriment concerning source and amount. Selected details of this problem are presented in this paper, in order to provide a conceptual background to understand the problem itself and to interprete the characteristics of the currently available assessment methodologies. The existing methodologies are summarized, their principles, characteristics, and application are illustrated by means of an example. From the application results, a comparison of the mentioned methodologies is shown to point out advantages and differences. In the framework of the conference this paper could start and support a discussion about the assigment of responsibilities related to power quality disturbances propagation and improvements of the existing methodologies.