Two decades of fast-paced innovation have improved the spatial resolution of fluorescence microscopy to enable molecular resolution with low invasiveness and high specificity. Fluorescence microscopy also enables scientists and clinicians to map and quantitate the physico-chemical properties (e.g., analyte concentration, enzymatic activities and protein-protein interactions) of biological samples. But the biochemical resolving power of fluorescence microscopy is not as well-optimized as its spatial resolution. Current techniques typically observe only the individual properties of fluorescence, thus limiting the opportunities for sensing and multiplexing. Here, we demonstrate a new imaging paradigm — Hyper Dimensional Imaging Microscopy (HDIM) — that quantifies simultaneously and efficiently all the properties of fluorescence emission (excited state lifetime, polarization and spectra) in biological samples, transcending existing limitations. Such simultaneous detection of fluorescence features maximizes the biochemical resolving power of fluorescence microscopy, thereby providing the means to enhance sensing capabilities and enable heavily multiplexed assays. Just as multi-dimensional separation in mass-spectroscopy and multi-dimensional spectra in NMR have empowered proteomics and structural biology, we envisage that HDIM spectra of unprecedented dimensionality will catalyse advances in systems biology and medical diagnostics.