a b s t r a c tAssessment and evaluation methodologies as well as combinations of them, for modelling of Human-Robot Interaction (HRI), are reviewed extensively and thoroughly in this paper. However, based on the types of robots and the kinds of interactions involved in the modelling of HRI, we concentrate just on the assistive social robot types. A comprehensive review has been done on each of these extensive evaluation and assessment methodologies applied for testing the usability of assistive social robots, user acceptance towards robots and robot acceptance in terms of behavioural adaptation during the HRI. The evaluation methodologies are reviewed based on the primary and non-primary basis, while the assessment methodologies are reviewed based on the type(s) of modelling approaches. We then discussed the weaknesses, strengths and uniqueness of each type of the past research work done on the evaluation and assessment methodologies. Comparison and contrast tables are also illustrated. Lastly, this paper provides our recommended directions, new vision, as well as our inspirations and new insights for future researches by highlighting the key areas for enhancing each of the past evaluation and assessment methodologies so that a better modelling approach for HRI can be achieved. Contributions of this review paper are also discussed thoroughly.