When used by the German Army, T-34s were designated Panzerkampfwagen T-34-76 747 (r).
They were in great demand as loot, but their silhouette and sound were so distinctive that they attracted German anti-tank fire like magnets.
Basically, T-34s were shot at on sight. To minimise the danger from friendly fire, extra-large German markings were painted on the turrets and flags were draped over the top of the turret or the hull to stop attacks from German planes.
Many T-34s - without turrets - provided excellent service as towing vehicles.
But ultimately, they were only a burden on the German repair facilities as the T-34 also had serious drawbacks.
In the role of command-vehicle, it was inferior to the German Panzer III and IV, because the space in the turret with the shorter gun was very limited, with the longer one it was inadequate by German standards .

To aim the gun, the turret was rotated by electric motors into roughly the right position, but fine adjustment had to be done manually.
The earlier turret was staffed by only two men, the commander (also acting as gunner) and the loader. Having to full-fill both roles limited the commander's effectiveness.
The recalcitrant gearbox made changing gear particularly difficult - this was the second biggest weakness of the Soviet battle tanks.
Most undamaged captured T-34 and KW tanks were abandoned due to clutch failure.

Special thanks to Dierk Schmidt, UK

Source: Spielberger, Beute-Kraftfahrzeuge und -Panzer der deutschen Wehrmacht, Motorbuch-Verlag