Inorganic nanocrystals with well–defined shapes are important for understanding basic size–dependent scaling laws, and may be useful in a wide range of applications. Methods for controlling the shapes of inorganic nanocrystals are evolving rapidly. This paper will focus on how we currently control the shape of nanocrystals and this will be illustrated using CdSe and Co nanocrystals as examples for semiconductors and for metals. These materials show a more pronounced variation of fundamental properties with aspect ratio. However, to take advantage of these shape–dependent properties in possible applications, several challenges need to be overcome. Issues such as alignment, high quantum yield and photostability and precise control of three–dimensional structures need to be addressed. These challenges, as well as several potential applications, will be described briefly.