The amount of generated and analyzed data is ever increasing, and processing such large data sets can take too long in situations where time-to-decision or fluid data exploration are critical. Progressive visual analytics (PVA) has recently emerged as a potential solution that allows users to analyze intermediary results during the computation without waiting for the computation to complete. However, there has been limited consideration on how these techniques impact the user. Based on discussions from a Dagstuhl seminar held in October 2018, this paper characterizes PVA users by their common roles, their main tasks, and their distinct focus of analysis. It further discusses cognitive biases that play a particular role in PVA. This work will help PVA visualization designers in devising systems that are tailored for their specific target users and their characteristics.