About 80 eclipsing binaries are known to be components of multiple-star systems. This is less than 2% of all known eclipsing-binary systems, but the actual total is certainly much higher than this, as the majority of stars under review are in fairly bright, well-studied systems. Triple-star systems are by far the most common of these, but one system in five is a quadruple or higher-order system. Quadruple systems include both systems of hierarchy 2 (two widely spaced pairs, e.g., BV+BW Draconis) and hierarchy 3 (e.g., r] Orionis). V772 Herculis and DN Ursae Majoris are in quintuple systems, and HR 3337 and the system that contains GZ Andromedae may also be quintuple. Castor, which contains the eclipsing binary YY Geminorum, is a very rare example of a sextuple-star system. Also considered are eclipsing binaries in compact star clusters such as SZ Camelopardalis and the two binaries in the Trapezium, BM Ori and V 1016 Ori. The most frequently encountered type of eclipsing binary to be found in multiple-star systems is that composed of two early-type (B5 or earlier) stars. Nearly all of the very close triple systems which have eclipsing-binary components are of this type. W UMa-type stars are also well represented among the multiple-star systems containing eclipsing binaries, but some other types are not. The RS Canum Venaticorum stars occur less frequently as components of multiple-star systems, and cataclysmic binaries appear to occur only very rarely as components of these systems. The physical and orbital properties of the multiple star systems are discussed in some detail in cases where the data are fairly complete, but it must be noted that many of the visual pairs have periods of revolution which are much too long to permit reliable determination of orbits. In triple-star systems with eclipsing binaries the ratio of P 2 /P x ranges from less than 10 (for A Tauri) to more than 10 7 in some cases. The questions of co-planarity of orbits and the membership of components in multiple-star systems are also considered.