Multidimensional photography can capture optical fields beyond the capability of conventional image sensors that measure only two-dimensional (2D) spatial distribution of light. By mapping a high-dimensional datacube of incident light onto a 2D image sensor, multidimensional photography resolves the scene along with other information dimensions, such as wavelength and time. However, the application of current multidimensional imagers is fundamentally restricted by their static optical architectures and measurement schemes-the mapping relation between the light datacube voxels and image sensor pixels is fixed. To overcome this limitation, we propose tunable multidimensional photography through active optical mapping. A high-resolution spatial light modulator, referred to as an active optical mapper, permutes and maps the light datacube voxels onto sensor pixels in an arbitrary and programmed manner. The resultant system can readily adapt the acquisition scheme to the scene, thereby maximising the measurement flexibility. Through active optical mapping, we demonstrate our approach in two niche implementations: hyperspectral imaging and ultrafast imaging.