The resolution of focused-ion-beam (FIB) microscopes, whether analytical or processing ones, is known to be determined by three main factors: (i) the size of a Gaussian (ideal) image of the ion source, (ii) the ion-optical aberrations, and (iii) the scattering of primary ions and secondary particles (both ions and electrons) in the target. This paper shows that each of them can be significantly reduced owing to recent advances in the field. These are (i) innovative field-ionization ion sources with a sub-1-nm effective emission area and improved brightness and ion-energy spread, (ii) the concept of a combined electromagnetic mirror for correcting axial aberrations in ion optics, and (iii) fresh data on the collision of low-energy He+ ions with a pure-metal surface and on the deceleration of low-energy O2+ ions in diamond. On this basis, a new concept of FIB microscope is proposed and discussed that is capable of operating in both analytical and processing mode, and offers better resolution by reducing all of the above-mentioned factors. It is shown that the combined electromagnetic mirror proposed enables one to achieve a 1.6-and a 1.5-nm resolution in analytical and processing mode, respectively, when only chromatic aberration is corrected. With perfect axial-aberration correction, a 0.6-and a 1-nm resolution should be attainable in analytical and processing mode, respectively.