Single-pixel detectors are popular devices in optical sciences because of their fast temporal response, high sensitivity, and low cost. However, when being used for imaging, they face a fundamental challenge in acquiring high-dimensional information of an optical field because they are essentially zero-dimensional sensors and measure only the light intensity. To address this problem, we developed a cascaded compressed-sensing single-pixel camera, which decomposes the measurement into multiple stages, sequentially reducing the dimensionality of the data from a high-dimensional space to zero dimension. This measurement scheme allows us to exploit the compressibility of a natural scene in multiple domains, leading to highly efficient data acquisition. We demonstrated our method in several demanding applications, including enabling tunable single-pixel full-waveform hyperspectral light detection and ranging (LIDAR) for the first time.