The resolution of any linear imaging system is given by its point spread function (PSF) that quantifies the blur of an object point in the image. The sharper the PSF, the better the resolution is. In standard fluorescence microscopy, however, diffraction dictates a PSF with a cigar-shaped main maximum, called the focal spot, which extends over at least half the wavelength of light (lambda = 400-700 nm) in the focal plane and >lambda along the optical axis (z). Although concepts have been developed to sharpen the focal spot both laterally and axially, none of them has reached their ultimate goal: a spherical spot that can be arbitrarily downscaled in size. Here we introduce a fluorescence microscope that creates nearly spherical focal spots of 40-45 nm (lambda/16) in diameter. Fully relying on focused light, this lens-based fluorescence nanoscope unravels the interior of cells noninvasively, uniquely dissecting their sub-lambda-sized organelles.