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Winds measured by lidar from the Aeolus satellite are compared with winds measured by two ground-based radars, MARA in Antarctica (70.77° S, 11.73° E) and ESRAD (67.88° N, 21.10° E) in Arctic Sweden. Aeolus is a demonstrator mission to test whether winds measured by Doppler lidar from space can have sufficient accuracy to contribute to improved weather forecasting. A comprehensive programme of calibration and validation has been undertaken following the satellite launch in 2018 but, so far, direct comparison with independent measurements from the Arctic or Antarctic regions have not been made. The comparison covers heights from the low troposphere to just above the tropopause. Results for each radar site are presented separately for Rayleigh (clear) winds, Mie (cloudy) winds, summer and winter, and ascending and descending satellite tracks. Horizontally-projected line-of-sight (HLOS) winds from Aeolus, for passes within 100 km from the radar sites, are compared with HLOS winds calculated from one-hour averaged radar horizontal wind components. The agreement in most data subsets is very good, with no evidence of significant biases (< 1 m s-1). Possible biases are identified for two subsets, about -2 m s-1 for MARA/Rayleigh/descending/winter winds, about 3 m s-1 for ESRAD/Mie /ascending /winter , but these are only marginally significant. A robust significant bias of about 6 m s-1 is found for MARA/Mie/ascending/summer winds. There is also some evidence for increased random error (by about 1 m s-1) for all of the Aeolus winds at MARA in summer compared to winter. This might be related to the presence of sunlight scatter over the whole of Antarctica as Aeolus transits across it during summer. [ABSTRACT FROM AUTHOR]