What are the left-handed media and what is interesting about them?

We review the intensively discussed ideas about wave propagation and refraction in media where both electric permittivity and magnetic permeability are negative. The criticism against negative refraction as violating the causality principle is considered. Starting from the initial wave equations, refraction of beams at the boundary of a left-handed medium is analyzed. The physics of a perfect lens formed by a flat layer of a left-handed material is considered.