We present cleared-tissue axially swept light-sheet microscopy (ctASLM), which enables isotropic, subcellular resolution imaging with high optical sectioning capability and a large field of view over a broad range of immersion media. ctASLM can image live, expanded, and both aqueous and non-aqueous chemically cleared tissue preparations. Depending on the optical configuration, ctASLM provides up to 260 nm of axial resolution, a three to tenfold improvement over confocal and other reported cleared-tissue light-sheet microscopes. We imaged millimeter-scale cleared tissues with subcellular three-dimensional resolution, which enabled automated detection of multicellular tissue architectures, individual cells, synaptic spines and rare cell-cell interactions.