A review on the Big Data in Astronomy and Space Sciences; all-sky and large-area astronomical surveys and their catalogued data over the whole range of electromagnetic spectrum, from gamma-ray to radio, coming from both ground-based and space telescopes, as well as most important surveys giving optical images, proper motions, variability and spectroscopic data will be presented, as well as data coming from Space Sciences; both from Earth and Space explorations. Most important astronomical databases and archives are reviewed as well. They are powerful sources for many-sided efficient research using the Astrophysical Virtual Observatory (AVO) environment. It is shown that using and analysis of Big Data accumulated in astronomy lead to many new discoveries. It is also important that Astronomy plays a leading role in the development of inter- and multi- disciplinary sciences; Astrochemistry, Astrobiology, Astrogeology, Space Research, Astroinformatics, Astrostatistics, as well as Archaeoastronomy and Astronomy in Culture. The exchange of data between science disciplines makes possible new research and better understanding of the Universe. The International Science Council (ISC) World Data System (WDS) maintains various data supporting joint research and synergy of efforts by scientists of various fields.