We present a brief description of a joint Russian-Korean project abbreviated as EXPLANATION (EXoPLANet And Transient events InvestigatiON). The project is aimed at a massive photometric, speckle-interferometric, spectral, and radio bolometric search for non-stationary events in the Universe, as well as the study of exoplanets. The core of the project consists of several 0.07-2.5-m optical telescopes, 6-m telescope BTA and a six-hundred-meter radio telescope RATAN-600 of the Special Astrophysical Observatory of RAS (Russia), Moscow State University observatory (Russia), Kourovka Observatory (Russia), Crimean Astrophysical Observatory (Crimea), Korea Astronomy and Space Science Institute (Republic of Korea). We discuss the philosophy of the project and its instrumentation, as well as the first obtained results. In this paper we report the results related to the detection of several types of transient events and the study of exoplanets.