There has been a systematic progression of knowledge, over the past 10 years, concerning the atomic arrangements and compositions at surfaces of bulk quasicrystals. Our group has been particularly involved in studying surfaces of the icosahedral aluminum-rich phases, both in ultrahigh vacuum and in air. The understanding of the surface structure of these materials is currently at a point where, we believe, it can be used as a springboard toward understanding more complex phenomena. Following a review of the picture that has evolved for the native surfaces in vacuum and in air, we will discuss more recent results for friction, wetting, and epitaxy.