Bands of Ukrainian soldiers fighting to take back territory on the eastern bank of the Dnipro River, an area long controlled by Russia, have been bombed by Russian warplanes, assaulted by Russian infantry and stalked by drones.

Still, battered and outgunned, the Ukrainian forces have managed to hold onto a handful of positions across the river for more than a month and are expanding their assaults on Russian forces there to target their vital supply lines.

The ultimate objectives of the Ukrainian campaign remain unclear: Is it aimed mainly at unbalancing Russian forces — using limited assaults to force the Kremlin to move troops to the area, hoping to create weaknesses along other parts of the front? Or does Ukraine have more ambitious objectives, like trying to mount a major cross-river assault aimed at taking back a substantial amount of territory and dramatically reshaping a front line that has barely moved in a year?

Many Western military analysts have voiced skepticism that Ukraine can establish the kind of bridgehead that would allow its forces to move artillery and heavy armor across the river, which they would need to carry out large-scale offensive operations.

Still, the sustained attacks could prove difficult for Russia, especially if Ukraine can interfere with critical Russian supply lines. Whatever the Ukrainian intentions, the marshy wetlands along the Dnipro are simmering.

Here is a brief look at how the fighting has evolved, where things stand, and the risks and rewards should Ukraine attempt the most ambitious battlefield river crossing since World War II.