  This progress report covers recent developments in the area of quantum
randomness, which is an extraordinarily interdisciplinary area that belongs not
only to physics, but also to philosophy, mathematics, computer science, and
technology. For this reason the article contains three parts that will be
essentially devoted to different aspects of quantum randomness, and even
directed, although not restricted, to various audiences: a philosophical part,
a physical part, and a technological part. For these reasons the article is
written on an elementary level, combining very elementary and non-technical
descriptions with a concise review of more advanced results. In this way
readers of various provenances will be able to gain while reading the article.
