The Russian retreat

 ISW:

The Russian military has likely decided to withdraw fully from its positions around Kharkiv City in the face of Ukrainian counteroffensives and the limited availability of reinforcements. Russian units have generally not attempted to hold ground against counterattacking Ukrainian forces over the past several days, with a few exceptions. Reports from Western officials and a video from an officer of the Donetsk People’s Republic (DNR) indicate that Moscow is focused on conducting an orderly withdrawal and prioritizing getting Russians back home before allowing proxy forces to enter Russia rather than trying to hold its positions near the city.

Ukraine thus appears to have won the Battle of Kharkiv. Ukrainian forces prevented Russian troops from encircling, let alone seizing Kharkiv, and then expelled them from around the city, as they did to Russian forces attempting to seize Kyiv. Ukrainian forces will likely attempt to disrupt at least the westernmost of the ground lines of communication (GLOCs) between Belgorod and Russian forces concentrated around Izyum, although Russia is using several GLOCs, including some further away from current Ukrainian positions than any Ukrainian counteroffensive is likely to reach soon. The terrain east of current Ukrainian positions may also favor the Russians attempting to defend their GLOCs, as large water features canalize movement and create chokepoints that the Ukrainians would have to breakthrough.

Russian troops continued efforts to advance all along the periphery of the Izyum-Donetsk city salient but made little progress. Russian forces attempted a ground offensive from Izyum that made no progress. We had previously hypothesized that Russia might give up on attempts to advance from Izyum, but the Russians have either not made such a decision or have not fully committed to it yet.[1] Small-scale and unsuccessful attacks on the southern end of the salient near Donetsk City continued but made no real progress.

The main Russian effort continues to be the attempt to encircle Severodonetsk and Lysychansk from the north and from the south. Russian troops attacking from Popasna to the north made no significant progress in the last 24 hours. Russian forces coming north-to-south have failed to cross the Siverskyi Donets River and taken devastating losses in their attempts. The Russians may not have enough additional fresh combat power to offset those losses and continue the offensive on a large enough scale to complete the encirclement, although they will likely continue to try to do so.

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Where they are not retreating, they have not handled resistance very well unless they are committing war crimes.  The Russian troops do not appear to be well trained or well led. 

See, also:

Russian morale, unit cohesion 'remains a problem' as Moscow makes slow gains in Donbas: US official

Ukrainian artillery is blocking Russian efforts to gain momentum in the Donbas