Robotic process automation (RPA) is an emerging technology that allows organizations automating repetitive clerical tasks by executing scripts that encode sequences of fine-grained interactions with Web and desktop applications. Examples of clerical tasks include opening a file, selecting a field in a Web form or a cell in a spreadsheet, and copy-pasting data across fields or cells. Given that RPA can automate a wide range of routines, this raises the question of which routines should be automated in the first place. This paper presents a vision towards a family of techniques, termed robotic process mining (RPM), aimed at filling this gap. The core idea of RPM is that repetitive routines amenable for automation can be discovered from logs of interactions between workers and Web and desktop applications, also known as user interactions (UI) logs. The paper defines a set of basic concepts underpinning RPM and presents a pipeline of processing steps that would allow an RPM tool to generate RPA scripts from UI logs. The paper also discusses research challenges to realize the envisioned pipeline.