Improving the resolution and sensitivity in all-optical microscopy and spectroscopy is inevitably one of the most important challenges in contemporary optical and nanoscience. Here, we discuss a novel approach, plasmonic nanofocusing, towards broadband, coherent all-optical microscopy with ultrahigh temporal and spatial resolution. The conceptual idea is to launch radially symmetric surface plasmon polariton modes onto the shaft of a sharp, conical metal taper. While propagating towards the apex of the pointed taper, the spatial extent of the plasmonic mode gradually shrinks, from several microns in diameter to a spot size of less than 10 nm at the pointed apex of the conical taper. Concomitantly, the local field amplitude of the plasmon mode gradually increases, resulting in a pronounced field enhancement at the apex and -thus -a bright and spatially isolated coherent light source with dimensions far below the diffraction limit. In this review, we characterize the optical properties of such three-dimensional conical metal tapers and demonstrate nanofocusing of radially symmetric plasmon modes. We use this nanolight source for coherent light scattering spectroscopy and demonstrate the sensitivity enhancement resulting from the pronounced spatial field confinement. It is shown that such off-resonant plasmonic nanoantennas facilitate the creation of nanofocused light spots with few-cycle time resolution. As a first application of this ability to nanolocalize ultrashort plasmon wavepackets, we demonstrate remotely-triggered multiphoton-induced photoemission from the very apex of the taper and implement this novel ultrafast electron gun in a point-projection electron microscope. Our results not only indicate the favourable optical properties of this plasmonic nanolens but also suggest that it may find interesting applications in ultrafast scanning optical spectroscopy and might enable new types of ultrafast electron holography and scanning tunnelling microscopy.