Successful medical conversations need practice. In medical education, students practice medical conversations with trained actors, who learn their role with the help of scripts with realistic yet not real patient histories. Given restricted resources, the number of training opportunities available during medical education is limited. This PhD thesis explores how social robots can support the training of students in conducting medical conversations. Specifically, it explores how automatic speech processing technologies can identify and model aspects of effective medical interactions. One such core aspect is to identify whether there is mutual understanding between the patient and the medical professional, a not trivial task in medical conversations. For model development, this thesis uses data from interactions between students and trained actors recorded at the Medical University of Graz. These recordings, along with accompanying scripts for the actors, structured questionnaires from observing students, and metadata (e.g., illness type, age), provide rich data for analysis. One example application of this work is enabling social robots to simulate patient conversational behaviors accurately, providing realistic interaction experiences and natural feedback to medical trainees.