In the field of law there is an absolute need for summarizing the texts of court decisions in order to make the content of the cases easily accessible for legal professionals. During the SALOMON and MOSAIC projects we investigated the summarization and retrieval of legal cases. This article presents some of the main findings while integrating the research results of experiments on legal document summarization by other research groups. In addition, we propose novel avenues of research for automatic text summarization, which we currently exploit when summarizing court decisions in the ACILA project. Techniques for automated concept learning and argument recognition are here the most challenging.