We analyse the problem with a charge intersecting the interface between ordinary medium and 'left-handed' one. Both the case of semi-infinite media and the case of a cylindrical waveguide are considered. We describe exact and asymptotic approaches for investigation of the electromagnetic field. We note features of spatial radiation due to unusual properties of 'left-handed' medium. In particular, the effect of 'reversed Cherenkov-transition radiation' (RCTR) is demonstrated both analytically and numerically.