The discovery of quasicrystals in 1982 signaled the beginning of a remarkable scientific revolution, in which some of the most basic notions of condensed matter physics and material science have undergone a thorough reexamination. Two and a half decades later, the field continues to intrigue
us with scientific puzzles, surprising discoveries, and new possibilities for applications. I will focus on some current issues from my own research - including soft matter quasicrystals and photonic applications based on metamaterials - but only after giving a concise overview for nonspecialists
of what quasicrystals are, and why their discovery was so important.