Recent advances in super-resolution fluorescence microscopy based on single-molecule imaging have led to ~10 nm spatial resolution and exciting science. We are developing new approaches to advance beyond the structural (shape) information offered by existing super-resolution methods, and reveal multidimensional information of intracellular functional parameters, including chemical polarity, diffusivity, and reactivity, with nanoscale resolution and single-molecule sensitivity. To this end, we have been developing new strategies to perform high-throughput, multidimensional single-molecule spectroscopy in the wide-field. In particular, with spectrally resolved SMLM, we encoded functional parameters into the emission spectra of single probe molecules, and so unveiled rich, nanoscale functional and compositional heterogeneities in the membranes of live mammalian cells and in phase-separated surface processes. With single-molecule displacement/diffusivity mapping (SMdM), we mapped out intracellular diffusivity with unprecedented spatial resolution and fidelity, and hence discovered that diffusion in the mammalian cytoplasm and nucleus are both spatially heterogeneous at the nanoscale, and identified the net charge of the diffuser as a previously overlooked, key determinant of diffusion rate. By adding remarkably rich functional dimensions to the already powerful super-resolution microscopy, we thus open up new ways to reveal fascinating local heterogeneities in both live cells and chemical systems.