4H-SiC Bipolar Junction Transistors (BJTs) and hybrid Darlington Transistors with 10 kV/10 A capability have been demonstrated for the first time. The SiC BJT (chip size: 0.75 cm2 with an active area of 0.336 cm2) conducts a collector current of 10 A (~ 30 A/cm2) with a forward voltage drop of 4.0 V (forced current gain βforced: 20) corresponding to a specific on-resistance of ~ 130 mΩ•cm2 at 25°C. The DC current gain, β, at a collector voltage of 15 V is measured to be 28 at a base current of 1 A. Both open emitter breakdown voltage (BVCBO) and open base breakdown voltage (BVCEO) of ~10 kV have been achieved. The 10 kV SiC Darlington transistor pair consists of a 10 A SiC BJT as the output device and a 1 A SiC BJT as the driver. The forward voltage drop of 4.5 V is measured at 10 A of collector current. The DC forced current gain at the collector voltage of 5.0 V was measured to be 440 at room temperature.