In this paper we present a primer on the state-of the-art of existing maturity models (MMs) for eLearning. By means of a traditional qualitative literature review, 29 different models are identified. Next, they are analysed and classified on the basis of a framework of 20 common properties derived from general theory on MMs, considering aspects related to their definition, structure and practical use. Results of the analysis suggest that existing eLearning MMs mainly address problems linked to eLearning management and organization at institutional level, educational technology, instructional design and faculty staff professional development. However, they tend to provide relatively moderate support for being effectively applied in practice, which clearly compromises and dismisses their power and utility as prescriptive tools for quality improvement. Our findings contribute to the current body of knowledge on eLearning by providing improved understanding, visibility, transparency and traceability of eLearning MMs designed to date, which may be of interest to both practitioners and researchers