Three days ago, Ukraine launched a surprise offensive into Russian territory, by far the largest of its kind since the start of the war in 2022 (previous incursions were by small militia groups who only stayed 2 or 3 days at most and captured maybe one border village). To date that they've managed to capture around 100-200 square kilometers of Russian territory.
Early into the attack, Russia falsely claimed to have repelled it. They've since repeated that claim several times as the area under Ukrainian control expands. Russian forces have retreated upon encountering the Ukrainians, and Ukraine's best mobile warfare unit is at the helm of this operation.
They've already captured the town of Sudzha, through which flows a Russian pipeline that supplies Europe (or at least it did before the war; I don't know if it still does today). If they can keep up their present momentum, they should be entering the city of Lgov by the end of today. Lgov has a population of about 17,000 and is a fairly major railway hub inside Russia. Furthermore Lgov is a 45 kilometer drive from Kursk, the capital of Kursk Oblast (population 415,000). Objects traveling in a straight line, such as artillery shells, would have to travel a much less than 45-km distance to strike Kursk from Lgov; for context, 45 kilometers is 28 miles.
It's 50/50, then, that by the end of today Ukraine will be able to bombard a Russian city about the size of New Orleans with at least a handful of artillery pieces. And depending on how incompetent the Russian response continues to be they might even capture said Russian city the size of New Orleans at some point in the near future. In this best case scenario, we are talking roughly half a million Russians living under Ukrainian occupation. Half a million Russian hostages whose lives and freedom Ukraine is able to use as a bargaining chip. The whole debacle would, if nothing else and even if short lived, be a catastrophic blow to Putin's image as a man able to protect ordinary Russians from foreign threats.