Robots that support humans by performing useful tasks (a.k.a., service robots) are booming worldwide. In contrast to industrial robots, the development of service robots comes with severe software engineering challenges, since they require high levels of robustness and autonomy to operate in highly heterogeneous environments. As a domain with critical safety implications, service robotics faces a need for sound software development practices. In this paper, we present the first large-scale empirical study to assess the state of the art and practice of robotics software engineering. We conducted 18 semi-structured interviews with industrial practitioners working in 15 companies from 9 different countries and a survey with 156 respondents from 26 countries from the robotics domain. Our results provide a comprehensive picture of (i) the practices applied by robotics industrial and academic practitioners, including processes, paradigms, languages, tools, frameworks, and reuse practices, (ii) the distinguishing characteristics of robotics software engineering, and (iii) recurrent challenges usually faced, together with adopted solutions. The paper concludes by discussing observations, derived hypotheses, and proposed actions for researchers and practitioners.