Lightning is inherent phenomenon of our life, however, it brings a big variety of surprises. The multi-disciplinary project “Lightning and thunderstorms: physics and effects” accumulates in the Institute of Applied Physics of RAS the abilities and efforts of several Russian scientific teams dealing with fundamentals and applications of atmospheric electricity and lightning under supervision of V.A.Rakov - Professor and Co-Director of the International Center for Lightning Research and Testing, University of Florida, USA. The Project researches cover a number of fundamental, still poorly understood problems, important for practical applications: lightning initiation conditions, streamer-leader formation, thunderstorm electrification and nowcasting, transient luminous events in the atmosphere, X-ray and gamma-ray flashes in the atmosphere correlated with lightning flashes, chemical effects of lightning, the role of lightning in the global electric circuit and the Earth's climate system.