Abstract: Superconducting circuits based on Josephson junctions can exhibit macroscopic quantum coherence. Quantum computation with superconducting circuits is one of the most important research directions in the field of quantum information. Moreover, the study of the physical properties of superconducting circuits is an interdisciplinary area of both condensed matter physics and quantum optics. A brief overview is presented of the main results and advancements achieved so far, as well as future prospects, in the area of superconducting quantum computation.