I've included a map at he bottom to help us understand what's going on and where.
Ukraine launched a series of offensive operations that started on August 29th in the south. This was no surprise and Russia had moved a lot of troops from the north to block any Ukrainian attacks in Kherson province or Donbas to the east.There's more information at the link. Here's a map that shows the status of forces as of 9/21:
All this turned out to be a deception and on September 6 Ukraine launched a more powerful surprise offensive in the northeast (Kharkiv province). Many Russian units panicked and fled when they realized they might be surrounded. This included units falling apart with troops abandoning tanks and other major items of equipment.
By the 11th Russia announced it was withdrawing from Kharkiv province.
The offensive spread to Donbas, causing a retreat from several towns that had come under Russian control in 2014. The offensive kept going in Kharkiv province with Ukrainian troops reaching the Russian border in many places.
Meanwhile the southern (Kherson province) offensive began on August 29th as a distraction, then expanded as Russian units panicked when they realized that Ukrainian HIMARS vehicles carrying GMLRS guided missiles were destroying the remaining bridges on the Dnieper River and trapping thousands of Russian troops.
The Ukrainian missiles also hit Russian supply storage sites leaving the trapped troops without ammunition, fuel and other supplies.
Ukrainian forces are now attacking on a broad front and expect to control all of Kherson province by the end of the year. This means major losses for the Russian in terms of troops captured or driven out of the area.
In addition, Ukraine will control most of the water supply for the Crimean Peninsula and control territory close enough to the Kerch Strait bridge to damage or destroy it with missiles or airstrikes. The Kerch Strait bridge was completed in 2014 at a cost of nearly four billion dollars. It is the main supply route between Russia and Crimea.
The only other rail line runs from Donbas to Crimea and is under attack by Ukrainian partisans.
Russia troop losses are another problem. Russia is unable to recruit enough troops to replace losses and a recent leaked report from the Russian Ministry of Finance completed in late August gave the Russian army’s “special military operations” in Ukraine some death toll numbers.
According to this report, the Russian government needs to allocate 361 billion rubles for the pensions of the fallen Russian troops, an average of about 7 million rubles per person, and a total of 48,759 dead.
Ukrainian military intel currently puts the Russian dead at about 54,000, a number many Westerners dismiss as inflated. Another Russian weakness that is largely ignored by Western media is the degree of corruption in the Russian military.
This has led to chronic shortages of essential supplies and equipment for the troops. This was particularly the case with thousands of Russian “reserve” troops recruited and financed by individual provinces. The central government ordered this mobilization but many provinces were unable to comply.
Those that did sent volunteers who were too old or out of shape for military service.
These men were attracted by the high bonuses and monthly pay promised. Those that survived their two months in Ukraine found that the money has not been deposited in their bank accounts as promised.
Conscripts are banned by law from serving combat outside Russia. Conscripts have also learned to avoid the deceptive offers to become a better paid contract soldier because it would make them eligible for service in Ukraine.
All this means Russia cannot obtain enough new troops to replace heavy losses in Ukraine. Ukrainian and NATO electronic monitoring of Russian communications confirms that replacements are lacking for troops lost (killed, wounded or captured) in combat.
Russian commanders are also concerned about their supply situation. They are not receiving enough ammunition, especially artillery shells and rockets. Food, clothing and medical supplies are inadequate, especially now that winter is coming and most of the troops will be at the front, not in barracks or other housing.
Hunger, cold and a lack of fire (artillery) support makes troops more willing to desert or surrender at the first opportunity.
Since this report Putin has issued orders to mobilize 300,000 men to serve in the military. The order has resulted in numerous protests and a mass exodus of young men fleeing Russia. Few want to fight in Putin's quixotic war.