A maturity model is a widely used tool in software engineering and has mostly been extended to domains such as education, health, energy, finance, government, and general use. It is valuable for evaluations and continuous improvement of business processes or certain aspects of organizations, as it represents a more organized and systematic way of doing business. In this paper, we only focus on college higher education. For this reason, we present a novel approach that allows detecting some gaps in the existing maturity models for universities, as they are not models that address the dimensions in their entirety. To identify these models and their validities, as well as a classification of models that were identified in universities, we carried out a systematic literature review on 27,289 articles retrieved with respect to maturity models and published in peer-reviewed journals between 2007 and 2020. We found 23 articles that find maturity models applied in universities, through exclusion and inclusion criteria. We then grouped these items into nine categories with specific purposes. We concluded that maturity models used in Universities move towards agility, which is supported by the semantic web.