Multidimensional coherent optical spectroscopy (MDCS) is an elegant and versatile tool to measure the ultrafast nonlinear optical response of materials. Of particular interest for semiconductor nanostructures, MDCS enables the separation of homogeneous and inhomogeneous linewidths, reveals the nature of coupling between resonances, and is able to identify the signatures of many-body interactions. As an extension of transient four-wave mixing (FWM) experiments, MDCS can be implemented in various geometries, in which different strategies can be used to isolate the FWM signal and measure its phase. I review and compare different practical implementations of MDCS experiments adapted to the study of semiconductor materials. The power of MDCS is illustrated by discussing experimental results obtained on semiconductor nanostructures such as quantum dots, quantum wells, microcavities, and layered semiconductors.