Summarization is an important natural language processing (NLP) task in identifying key information from text. For conversations, the summarization systems need to extract salient contents from spontaneous utterances by multiple speakers. In a special task-oriented scenario, namely medical conversations between patients and doctors, the symptoms, diagnoses, and treatments could be highly important because the nature of such conversation is to find a medical solution to the problem proposed by the patients. Especially consider that current online medical platforms provide millions of public available conversations between real patients and doctors, where the patients propose their medical problems and the registered doctors offer diagnosis and treatment, a conversation in most cases could be too long and the key information is hard to be located. Therefore, summarizations to the patients’ problems and the doctors’ treatments in the conversations can be highly useful, in terms of helping other patients with similar problems have a precise reference for potential medical solutions. In this paper, we focus on medical conversation summarization, using a dataset of medical conversations and corresponding summaries which were crawled from a well-known online healthcare service provider in China. We propose a hierarchical encoder-tagger model (HET) to generate summaries by identifying important utterances (with respect to problem proposing and solving) in the conversations. For the particular dataset used in this study, we show that high-quality summaries can be generated by extracting two types of utterances, namely, problem statements and treatment recommendations. Experimental results demonstrate that HET outperforms strong baselines and models from previous studies, and adding conversation-related features can further improve system performance.