We present physical motivations and advantages of the new gamma-observatory TAIGA (Tunka Advanced Instrument for cosmic ray physics and gamma-ray astronomy). TAIGA will be located in the Tunka valley, 50 km to the west of Lake Baikal, at the same place as the integrating air Cherenkov detector for cosmic rays Tunka-133. The TAIGA array is a complex, hybrid detector for ground-based gamma-ray astronomy for energies from a few TeV to several PeV as well as for cosmic ray studies from 100 TeV to several EeV. The array will consist of a wide angle Cherenkov array – TAIGA-HiSCORE with 5km2 area, a net of 16 IACT telescopes (with FOV of about 9.72°×9.72°) as well as muon and other detectors. We present the current status of the array construction.