Recent advances in the use of curved single crystal surfaces

In surface science, research traditionally employs macroscopically flat surfaces of single crystals. Curved surfaces have been applied more sporadically, but their history stretches back for many decades. Realization of the potential benefits and practical applications in surface physics and surface chemistry research progressed slowly in the 20th century. In more recent decades, research employing partial cylinders and dome-shaped crystals have found renewed interest. Modern surface sensitive techniques are being employed allowing the inherent large range of surface structures to reveal new insights. We briefly review the history, describe several types of surfaces and the range of structures they contain, suggest a notation for common types of curved surfaces, and discuss recent studies in more detail. We mainly focus on metal samples. We close with a short outlook.