Package structures are provided for integrally packaging antennas with semiconductor RFIC (radio frequency integrated circuit) chips to form compact integrated radio/wireless communications systems that operate in the millimeter-wave and terahertz frequency ranges. For example, a package structure includes an RFIC chip, and an antenna package bonded to the RFIC chip. The antenna package includes a glass substrate, at least one planar antenna element formed on a first surface of the glass substrate, a ground plane formed on a second surface of the glass substrate, opposite the first surface, and an antenna feed line formed through the glass substrate and connected to the at least one planar antenna element. The antenna package is bonded to a surface of the RFIC chip using a layer of adhesive material.