The principles of formation of antennas of diffraction radiation with flat surface in the millimeter wave radio band are considered. Such kinds of antennas are based on the effect of the conversion of volumetric electromagnetic waves into surface waves of a dielectric waveguide in an open electrodynamic structure. A brief description of the theoretical basis for the calculations and examples of the technical implementation of flat (2D) antennas of diffraction radiation in the W-band and Ka-band are presented; their parameters and areas of possible use are discussed. In the E-plane angle-to-frequency dependence of beam position is realized with coefficient near 0,9°/1% of frequency change. That makes it possible effective control of beam position in space (beam scanning along 1, or even along 2 axes). There was estimated that total active loss in such kind antennas is related to dielectric losses in the material of planar dielectric waveguide and to active losses at the elements of internal waveguide transitions in the ratio near (2: 1). Losses of first kind may be reduced due to implementation of novel dielectric materials providing the smallest dielectric loss (near as for the PTFE material) and appropriate mechanical rigidity at the same time. Active losses of the second kind may be reduced due to implementation of transitions on the base of super-size waveguides.