Three-dimensional (3D) shape measurements based on high-density point clouds are currently replacing conventional discrete coordinate measurements and are thus a new development trend in the field of geometric measurement. In addition to their narrow-sense manufacturing applications, the multi-spatial-resolution characteristics of high-density point clouds provide a broad range of applications in the operational monitoring of mechanical equipments or large engineering projects such as high-speed trains, aircrafts, and tunnels. However, unlike with the 3D shape measurement problem that occurs under static conditions in the field of manufacturing, for the measured objects in service state, new characteristics are required, including in-motion high-speed continuous extension of point clouds and high-resolution acquisition. The new problem of extendable surface measurements poses a major challenge to conventional measurement methods. One-dimensional image sensors, represented by line-scan CCD and CMOS, can collect images rapidly and continuously in motion, providing excellent hardware potential for 3D shape measurements to meet the requirements of high-speed, continuous, and high-density measurements. One-dimensional image sensors have been in regular development and attracted considerable interest in recent years. In this paper, the key technologies including parameter calibration, one-dimensional image matching, multi-sensor layout and synchronization, and motion error compensation are reviewed for high-resolution shape measurements of extendable surfaces based on one-dimensional images, and their possible developmental directions are discussed.