Robots increasingly interact with humans through touch, where people are touching or being touched by robots. Yet, little is known about how such interactions shape a user's experience. To inform future work in this area, we conduct a systematic review of 44 studies on physical human-robot interaction (pHRI). Our review examines the parameters of the touch (e.g., the role of touch, location), the experimental variations used by researchers, and the methods used to assess user experience. We identify five facets of user experience metrics from the questionnaire items and data recordings for pHRI studies. We highlight gaps and methodological issues in studying pHRI and compare user evaluation trends with the Human-Computer Interaction (HCI) literature. Based on the review, we propose a conceptual model of the pHRI experience. The model highlights the components of such touch experiences to guide the design and evaluation of physical interactions with robots and inform future user experience questionnaire development.