Microtubules organize into a set of distinct patterns with the help of associated molecules that control nucleation, polymerization, crosslinking, and transport. These patterns, alone or in combination with each other, define the functional architecture of the microtubule cytoskeleton in living cells. In vitro experiments of increasing complexity help understand, in combination with theoretical models, the basic mechanisms by which elementary microtubule patterns arise, how they are maintained, and how they position themselves with respect to the confining geometry of living cells.