Our world is evolving very rapidly, both from the technological point of view – with impressive advances in artificial intelligence and new hardware challenging longstanding PC hardware traditions, for example – and as a result of unexpected events. The year 2020 was quite exceptional, an annus horribilis, according to some. It is hard to disagree with this statement, but every dark cloud has a silver lining. 2020 was also the year that accelerated digital transformation beyond what could have been imagined in 2019. Vaccine development happened faster than would ever have been conceivable a year ago, digital payment became the norm for many people and e-commerce and online sales threatened brick and mortar shops. Employees were encouraged to work from home – with its advantages and disadvantages, videoconferencing became the de facto way to interact with both family and colleagues, schools were forced to experiment with distance learning. The list goes on. After living for over a year in an online world, most people will not return completely to the “old normal”. They will go for a combination of the “old normal” and things they discovered and experimented with in the circumstances forced upon us by COVID-19; they might keep their home office on some days, and be in the workplace on other days. Higher education will certainly also continue to offer online teaching. The rapidly evolving digital world has also had an impact on the HiPEAC Vision: updating it every two years no longer seems quite in keeping with the speed of the evolution of computing systems. Therefore, we decided to move from producing a large roadmap document every other year, to an agile, rapidly evolving electronic magazine-like set of articles. The HiPEAC Vision 2021 has two main parts: 1) A set of recommendations for the HiPEAC community. It will also introduce the second part of the Vision and will be updated periodically, or on particular occasions. 2) A set of “articles”, like in magazines, that will be regularly updated, the purpose of which is to support the set of recommendations, or to introduce new topics or situations. This will guarantee that the HiPEAC Vision keeps evolving and remains up to date. These articles are intended to be self-sufficient and can be read independently. They are grouped into four themes or dimensions: technical, business, societal and European. New articles will be added over the course of the years (and outdated ones might be removed). A further element of this new approach to the Vision is that the editorial board asked and will ask various authors to contribute to those articles. "is adds heterogeneity and a diversity of point of view that could be helpful for better analysis of the computing systems landscape as well as improve the quality of the recommendations.