Single-molecule localization microscopy (SMLM) is suitable for high resolution imaging in fixed samples. While it is live compatible, a number of applications remain challenging due to the tradeoff between temporal and spatial samplings, particularly when the system studied displays heterogenous protein densities or dynamic processes at different temporal scales. We aim to image biological samples at high speed thanks to a new approach to SMLM using an event-based sensor in place of scientific cameras (sCMOS/EMCCD). This will be particularly relevant to answer biological questions requiring time-resolved high resolution imaging of transient structures in living cells. Event-based sensors are affordable commercially-available matrices of independent, asynchronous pixels sensitive to intensity variations. Their response time is very fast and a given frame rate needs not be chosen before the experiment. This can be used to image processes at various dynamic scales, or to detect blinking molecules among overlapping fluorophores that stay in a bright state. After describing the working principle of such event-based sensor and the experimental setup used for SMLM, we explain how data acquisition and processing are achieved in practise. We then image fixed biological samples in the dSTORM regime (alpha-tubulin AF647), first at normal Point Spread Function (PSF) density, and then at high density where the PSFs overlap significantly, causing camera-based methods to fail. In such a situation, the event-based sensing allows detecting only the moment when a molecule turns on or off, making it distinguishable from other molecules emitting in its diffraction-limited vicinity. We explain how to compare the performances with camera-based approaches to highlight a vast increase of image resolution and fidelity compared to frame-based SMLM. We finally discuss possibilities of assessing multiscale diffusion in event-based Single Particle Tracking.