We have demonstrated high-speed operation of Josephson processors. They are, a 4-bit microprocessor, a 4-bit processor, and an 8-bit digital signal processor. In this paper, key technologies to realize these circuits are described from the view point of circuit design. The technologies are, high-speed logic gate, named MVTL (modified Variable Threshold Logic), and three-phase sinusoidal power supply system. The MVTL gate has large operating margin and high sensitivity. MVTL gate family consists of OR, AND, 2/3 Majority (MJ), and Timed Inverter (TI). Using these gates, we have designed a variety of processors. We operate the processors with three-phase power. Its waveform is sinusoidal with dc-offset. This power supply system needs no latch and regulator circuit. It makes the processor very simple and thus results in high-speed operation. To fabricate these processors, niobium junctions are very important, because they are reliable, uniform, controllable, and reproducible. High-speed gate, three-phase, power supply, and niobium junction are indispensable for high-speed Josephson processors.