ABSTRACT We study a suite of extremely high-resolution cosmological Feedback in Realistic Environments simulations of dwarf galaxies ($M_{\rm halo} \lesssim 10^{10}\rm \, M_{⊙ }$), run to z = 0 with $30\, \mathrm{M}_{⊙ }$ resolution, sufficient (for the first time) to resolve the internal structure of individual supernovae remnants within the cooling radius. Every halo with $M_{\rm halo} \gtrsim 10^{8.6}\, \mathrm{M}_{⊙ }$ is populated by a resolved stellar galaxy, suggesting very low-mass dwarfs may be ubiquitous in the field. Our ultra-faint dwarfs (UFDs; $M_{* }\lt 10^{5}\, \mathrm{M}_{⊙ }$) have their star formation (SF) truncated early (z ≳ 2), likely by reionization, while classical dwarfs ($M_{* }\gt 10^{5}\, \mathrm{M}_{⊙ }$) continue forming stars to z < 0.5. The systems have bursty star formation histories, forming most of their stars in periods of elevated SF strongly clustered in both space and time. This allows our dwarf with M*/Mhalo > 10−4 to form a dark matter core ${\gt}200\rm \, pc$, while lower mass UFDs exhibit cusps down to ${\lesssim}100\rm \, pc$, as expected from energetic arguments. Our dwarfs with $M_{* }\gt 10^{4}\, \mathrm{M}_{⊙ }$ have half-mass radii (R1/2) in agreement with Local Group (LG) dwarfs (dynamical mass versus R1/2 and stellar rotation also resemble observations). The lowest mass UFDs are below surface brightness limits of current surveys but are potentially visible in next-generation surveys (e.g. LSST). The stellar metallicities are lower than in LG dwarfs; this may reflect pre-enrichment of the LG by the massive hosts or Pop-III stars. Consistency with lower resolution studies implies that our simulations are numerically robust (for a given physical model).