The only way to visually observe cellular viscosity, which can greatly influence biological reactions and has been linked to several human diseases, is through viscosity imaging. Imaging cellular viscosity has allowed the mapping of viscosity in cells, and the next frontier is targeted viscosity imaging of organelles and their microenvironments. Here we present a fluorescent molecular rotor/FLIM framework to image both organellar viscosity and membrane fluidity, using a combination of chemical targeting and organelle extraction. For demonstration, we image matrix viscosity and membrane fluidity of mitochondria, which have been linked to human diseases, including Alzheimer's Disease and Leigh's syndrome. We find that both are highly dynamic and responsive to small environmental and physiological changes, even under non-pathological conditions. This shows that neither viscosity nor fluidity can be assumed to be fixed and underlines the need for single-cell, and now even single-organelle, imaging.