Owing to their high sensitivity and low noise, superconducting detectors are used for photon detection from microwave to high-energy particles. X-ray detection plays an important role in materials analysis, astronomy, and medical radiography, which require high efficiency as well as high energy resolution. However, traditional semiconducting detectors cannot fulfill these requirements. In this article, we review superconducting quantum detectors for X-ray detection, including transition-edge sensor(TES), superconducting tunneling junctions(STJs), kinetic inductance detectors(KIDs) and superconducting nanowire single-photon detectors(SNSPDs), and introduce the physical structures, working mechanisms, and device behaviors of these detectors. We also review their performances regarding X-ray detection and analyze their respective characteristics. According to recent progress and the requirements of various applications, possible improvement of superconducting detectors for X-rays are discussed.