High-energy cosmic rays impinging onto the atmosphere of the Earth initiate cascades of secondary particles: extensive air showers. Many of the particles in a shower are electrons and positrons. During the development of the air shower and by interacting with the geomagnetic field, the electromagnetic cascade creates radiation, which we detect at frequencies of tens of MHz with the LOFAR radio telescope in the Netherlands. After many years of struggling to understand the emission mechanisms, the radio community has achieved the breakthrough. We are now able to determine direction, energy, and type of the shower- inducing primary particle from the radio measurements. The large number of antennas at LOFAR allows us to have a high precision and very detailed measurements. We will elaborate on the shower reconstruction, a precise description of the intensity of the radio signal at ground level (at frequencies from 10 to 240 MHz), a precise measurement of the shape of the radio wavefront, and on the reconstruction of the shower energy.