Polymer-matrix composites containing continuous carbon fibers are the dominant lightweight structural materials. The monitoring of the damage is important for structural health monitoring and hazard mitigation. The monitoring of the strain is relevant to structural vibration control and security. This paper reviews the use of the composites themselves to sense their own damage and strain, thereby removing or reducing the need for embedded or attached sensors, which suffer from high cost and poor durability. Both damage and strain affect the volume electrical resistivity of a composite, thereby allowing the monitoring of damage and strain in real time by volume resistivity measurement. The contact resistivity of the interlaminar interface (i.e., the interface between the laminae) provides another attribute for monitoring. A configuration involving two crossply laminae provides a two-dimensional array of sensors and an x-y grid of electrical interconnections, thereby allowing spatial distribution sensing.