"In our largely unchanging radio Universe, a highly dynamic component was recently discovered: flashes of bright radio emission that last only milliseconds but appear all over the sky. Some of these radio bursts can be traced to intermittently pulsating neutron stars. Other bursts however, apparently originate far outside our Galaxy. Due to great observational challenges, the evolution of the neutron stars is not understood, while more importantly, the nature of the extragalactic bursts remains an outright mystery.My overall aim is to understand the physics that drives both kinds of brief and luminous bursts.My primary goal is to identify the highly compact astrophysical explosions powering the extragalactic bursts. My previous surveys are the state of the art in fast-transient detection; I will now increase by a factor of 10 this exploration volume. In real-time I will provide arcsec positions, 10,000-fold more accurate than currently possible, to localize such extragalactic bursts for the first time and understand their origin.My secondary goal is to unravel the unexplained evolution of intermittently pulsating neutron stars (building on e.g., my recent papers in Science, 2013), by doubling their number and modeling their population.To achieve these goals, I will carry out a highly innovative survey: the Apertif-LOFAR Exploration of the Radio Transient Sky. ALERT is over an order of magnitude more sensitive than all current state-of-the art fast-transient surveys.Through its novel, extremely wide field-of-view, Westerbork/Apertif will detect many tens of extragalactic bursts. Through real-time triggers to LOFAR I will next provide the precise localisation that is essential for radio, optical and high-energy follow-up to, for the first time, shed light on the physics and objects driving these bursts – evaporating primordial black holes; explosions in host galaxies; or, the unknown?"