Reports have circulated in the media that dozens of icons in Ukraine and Russia have suddenly started weeping in light of recent tensions between the two countries. However, the video news report circulated (above) was posted on September 27, 2013. Therefore, this phenomenon actually took place on the eve before the unrest that came to Ukraine, which began in November 2013 and escalated in January 2014. Since this video was posted by the actual news station, it is assumed the report was in fact made in late September 2013.
It thus appears that in September dozens of icons began weeping in Ukraine and Russia in various parishes and monasteries. The people wondered at the time what kind of heavenly sign this was, since signs like this have often taken place in history on the eve of large-scale disasters, such as, for example, the Russian Revolution of 1917. Due to the more recent revolutionary activity in Ukraine, it is interpreted now that this phenomenon is associated with it.
Among the locations of the weeping icons in Russia were Syktyvkar, Pechora, Rostov-on-Don, Novokuznetsk. In Ukraine they were in Odessa, Rivne and other locations.
It is not known if these icons have continued weeping.
Note: The images of weeping icons in the video is from an incident of weeping icons that took place in Belarus in 2005. I'm not sure why they are shown in this video. For information on this phenomenon from 2005, read here and here.