Most of the existing literature that deals with the digital divide in the educational system focuses either on schools or universities, but rarely do we see a vertical approach where the system is considered as a whole. In this paper we relate initiatives that aim to bridge the digital divide in the current situation in higher education. We discuss why policies that focus on infrastructures (e.g. laptops) are not the answer, as they mostly leave digital competences unattended, leading to (or not helping to amend) the digital void in universities in matters of skills. We end by proposing a general framework to define digital skills so that they are included in syllabuses at all stages of the educational path.