Optical imaging of the dynamics of living specimens involves tradeoffs between spatial resolution, temporal resolution, and phototoxicity, made more difficult in three dimensions. Here, however, we report that rapid three-dimensional (3D) dynamics can be studied beyond the diffraction limit in thick or densely fluorescent living specimens over many time points by combining ultrathin planar illumination produced by scanned Bessel beams with super-resolution structured illumination microscopy. We demonstrate in vivo karyotyping of chromosomes during mitosis and identify different dynamics for the actin cytoskeleton at the dorsal and ventral surfaces of fibroblasts. Compared to spinning disk confocal microscopy, we demonstrate substantially reduced photodamage when imaging rapid morphological changes in D. discoideum cells, as well as improved contrast and resolution at depth within developing C. elegans embryos. Bessel beam structured plane illumination thus promises new insights into complex biological phenomena that require 4D subcellular spatiotemporal detail in either a single or multicellular context.