Statistical studies of active galaxies (both AGN and Starburst) using large multi-wavelength data are presented, including new studies of Markarian galaxies, large sample of IR galaxies, variable radio sources, and large homogeneous sample of X-ray selected AGN. Markarian survey (the First Byurakan Survey) was digitized and the DFBS database was created, as the biggest spectroscopic database by the number of objects involved ( ~ 20 million). This database provides both 2D images and 1D spectra. We have carried out a number of projects aimed at revealing and multi-wavelength studies of active galaxies among optical, X-ray, IR and radio sources. Thousands of X-ray sources were identified from ROSAT, including many AGN (52% among all identified sources). IRAS PSC/FSC sources were studied having accurate positions from WISE and a large extragalactic sample was created for further search for AGNs. The fraction of active galaxies among IR-selected galaxies was estimated as 24%. Variable radio sources at 1.4 GHz were revealed by cross-correlation of NVSS and FIRST catalogues using the method introduced by us for optical variability. Radio-X-ray sources were revealed from NVSS and ROSAT for detection of new active galaxies. Big Data in astronomy is described that provide new possibilities for statistical research of active galaxies and other objects.