  Over the previous decade, many approaches for the modelling of radio emission
from cosmic ray air showers have been developed. However, there remained
significant deviations between the models, reaching from important qualitative
differences such as unipolar versus bipolar pulses to large variations in the
predicted absolute amplitudes of up to factors of 20. Only recently, it has
been realized that in the many models predicting unipolar pulses, a radio
emission contribution due to the time-variation of the number of charged
particles or, equivalently, the acceleration of the particles at the beginning
and the end of their trajectories, had not been taken into account. We discuss
here the nature of the underlying problem and demonstrate that by including the
missing contribution in REAS3, the discrepancies are reconciled. Furthermore,
we show a direct comparison of REAS3 and MGMR simulations for a set of
prototype showers. The results of these two completely independent and very
different modelling approaches show a good level of agreement except for
regions of parameter space where differences in the underlying air shower model
become important. This is the first time that two radio emission models show
such close concordance, illustrating that the modelling of radio emission from
extensive air showers has indeed made a true breakthrough.
