Higher Education Institutions (HEIs) are involved in an evolution to a new model of university called "digital university." This model implies not only adopting new technologies but also developing an organizational strategic transformation which includes information, processes, human aspects, and more. Because an organization's digital maturity correlates with the scope of its digital transformation efforts, this study aims to identify digital transformation initiatives (DTI) taken by HEIs, defining the new processes and technologies used to implement them. The main motivation is to have a real and clear vision of how universities are transforming themselves, discovering the most relevant DTI that they have applied and if they are doing it through an integrated plan aligned with a digital strategy, as recommended by experts. We conducted a Multivocal Literature Review, as methodology research, to include both academic and grey literature in the analysis. Main results show that the DTI implemented are primarily focused on "providing a quality and competitive education" (24% of 184 DTI from 39 different universities analyzed). Emerging technologies most frequently used are "advanced analytics" (23%), "cloud" (20%) and "artificial intelligence" (16% of total DTI). We conclude that HEIs are in the first steps to digital maturity as only 1 in 4 have a digital strategy and 56% have launched isolated DTI that are not integrated in a plan and do not have a high strategic return value to the organization.