Someone on the results page asked what the Yale interview entailed. To my knowledge the interview is required by all graduate programs (at Yale) and is used by the history department as a way to gauge interest. I was asked to talk about my interests, my current studies at oxford, past research experiences, who I worked with and how that impacted my work, etc. it was informal and honestly just an enjoyable chat. I followed up with questions about the structure of the program and source access.
Hope this info helps