With more and more meetings moving to a digital domain, meeting summarization has recently gained interest in both academic and commercial research. However, prior academic research focuses on meeting summarization as an offline task, performed after the meeting concludes. In this paper, we perform the first systematic study of online meeting summarization. For this purpose, we propose several policies for conducting online summarization. We discuss the unique challenges of this task compared to the offline setting and define novel metrics to evaluate latency and partial summary quality. The experiments on the AutoMin dataset show that 1) online models can produce strong summaries, 2) our metrics allow a detailed analysis of different systems' quality-latency trade-off, also taking into account intermediate outputs and 3) adaptive policies perform better than fixed scheduled ones. These findings provide a starting point for the wider research community to explore this important task.