This paper is devoted to EBG horn antennas. This novel type of all-dielectric horn antennas is based on complex hollow defects in woodpile structures and can be used for creating compact arrays and provide a promising solution for millimeter and terahertz devices. A novel concept of feeding EBG horn antennas via evanescent fields existing in periodic structures is presented. The principle of creating all-dielectric pyramidal horn antennas based on woodpile structure with hollow defects is proposed. Different horn antennas based on woodpile structures and characterized by large operating bandwidths and high levels of directivity and efficiency were designed, fabricated and measured.