A system that could reliably identify and sum up the most important points of a conversation would be valuable in a wide variety of real-world contexts, from business meetings to medical consultations to customer service calls. Recent advances in deep learning, and especially the invention of encoder-decoder architectures, has significantly improved language generation systems, opening the door to improved forms of abstractive summarization—a form of summarization particularly well-suited for multi-party conversation. In this paper, we provide an overview of the challenges raised by the task of abstractive meeting summarization and of the data sets, models, and evaluation metrics that have been used to tackle the problems.