Libraries, archives, and museums (LAM) have existed since Antiquity in many different sizes and forms, and these institutions are not always easy to define and to separate from each other. Since the turn of the millennium, LAM has frequently been used as an acronym for these institutions, indicating an increasing interest to consider them together, partly motivated by a perceived ongoing convergence between them. This article describes and discusses this issue from ancient times to the present with the focus on convergence and conceptual issues, with emphasis on the practices, debates, and research over the two last decades. Distribution of documents via the Internet has been a catalyst for renewed interest in the relations between the LAMs, where increased use of digital resources is claimed to blur the traditional borders between the institutions (labelled “digital convergence”). In the first decade after the millennium, the research agenda was marked by a limited focus on digital point of access portals for cultural heritage. Thereafter, the research agenda broadened. In addition to digital convergence, other kinds of convergence are a nascent topic for research, focusing on physical mergers, collaboration, shared professional practice, proximity in government agencies and an increasing dependency on common external trends, etc. LAM has also increasingly been the name for new educational programs and university departments, thus pointing towards LAM as a concept used about an emerging discipline or interdisciplinary field. There have formerly been attempts to construe a research field, which include these three kinds of institutions, and the notion LAM is more extended term than the study of these institutions, because each of them has developed research fields with a broader focus.