Computer literacy was a hot topic in academia and research during the 90's, as computer skills were being massively introduced in under-graduate and graduate programmes. At the time, the focus relied on designing courses with a relevant technological component and on the assessment of the acquisition of basic computer skills by students, as the growing market demands for tech-savvy employees' profile tended to increase. However, the preconception that younger generations are inherently able to interact with computer systems-being constantly surrounded by smartphones, tablets and any kind of digital device-computer illiteracy has become an issue for the so-called digital natives. In fact, the most relevant educational research streams have shifted towards the use of ICT as a tool to enhance learning, and to its effective integration for teaching and learning considering the need to increase large-scale education, leaving behind ICT as a core transversal skill needed for almost any job position available back then and nowadays. Computer literacy can thus be confused with the ability to find, evaluate, produce and communicate clear information through writing and other forms of communication on various digital platforms, while interacting with digital devices. Indeed, the most common end-user computer skills required for a great diversity of job occupations demands skills such as experience with word-processing and spreadsheet applications, which students tend to consider way too difficult. Thus, there is a paradox between a so called digital-literate and a computer-literate student/professional nowadays, given that a digitalliterate is not necessarily a computer-literate and, sometimes, unable to perform required, and essential, academic and professional tasks efficiently. In this paper we discuss the distinct domains of skills concerning computer literacy and digital literacy under the light of the so-called hard-skills and soft-skills, which are required for graduate students and professionals entering the labour market. We present results on a study conducted on ten different higher education courses regarding students' self-assessment of mastering computer literacy skills, the perceived relevance of acquiring these skills for academic and professional purposes and the perceived need to (re) introduce them in higher education training.