Weather radar has become an invaluable tool for monitoring rainfall and studying its link to hydrological response. However, when it comes to accurately measuring small-scale rainfall extremes responsible for urban flooding, many challenges remain. The most important of them is that radar tends to underestimate rainfall compared to gauges. The hope is that by measuring at higher resolutions and making use of dual-polarization radar, these mismatches can be reduced. Each country has developed its own strategy for addressing this issue. However, since there is no common benchmark, improvements are hard to quantify objectively. This study sheds new light on current performances by conducting a multinational assessment of radar's ability to capture heavy rain events at scales of 5 min up to 2 h. The work is performed within the context of the joint experiment framework of project MUFFIN (Multiscale Urban Flood Forecasting), which aims at better understanding the link between rainfall and urban pluvial flooding across scales. In total, six different radar products in Denmark, the Netherlands, Finland and Sweden were considered. The top 50 events in a 10- year database of radar data were used to quantify the overall agreement between radar and gauges as well as the bias affecting the peaks. Results show that the overall agreement in heavy rain is fair (correlation coefficient 0.7-0.9), with apparent multiplicative biases on the order of 1.2-1.8 (17 %- 44 % underestimation). However, after taking into account the different sampling volumes of radar and gauges, actual biases could be as low as 10 %. Differences in sampling volumes between radar and gauges play an important role in explaining the bias but are hard to quantify precisely due to the many post-processing steps applied to radar. Despite being adjusted for bias by gauges, five out of six radar products still exhibited a clear conditional bias, with intensities of about 1 %-2% per mmh-1. As a result, peak rainfall intensities were severely underestimated (factor 1.8-3.0 or 44 %- 67 %). The most likely reason for this is the use of a fixed Z-R relationship when estimating rainfall rates (R) from reflectivity (Z), which fails to account for natural variations in raindrop size distribution with intensity. Based on our findings, the easiest way to mitigate the bias in times of heavy rain is to perform frequent (e.g., hourly) bias adjustments with the help of rain gauges, as demonstrated by the Dutch C-band product. An even more promising strategy that does not require any gauge adjustments is to estimate rainfall rates using a combination of reflectivity (Z) and differential phase shift (Kdp), as done in the Finnish OSAPOL product. Both approaches lead to approximately similar performances, with an average bias (at 10 min resolution) of about 30% and a peak intensity bias of about 45 %.