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Antenna-on-chip (AoC) and antenna-in-package (AiP) solutions are studied for highly integrated millimeter-wave (mmWave) devices in wireless communications. First, the background, regulations, standard, and applications of 60-GHz wireless communications are briefly introduced. Then, highly integrated 60-GHz radios are overviewed as a basis for the link budget analysis to derive the antenna gain requirement. Next, in order to have deep physical insight into the AoC solution, the silicon substrate's high permittivity and low resistivity effects on the AoC efficiency are examined. It is shown that the AoC solution has low efficiency, less than 12% due to large ohmic losses and surface waves, which requires the development of techniques to improve the AoC efficiency. After that, the AiP solution and associated challenges such as how to realize low-loss interconnection between the chip and antenna are addressed. It is shown that wire-bonding interconnects, although inferior to the flip-chip, are still feasible in the 60-GHz band if proper compensation schemes are utilized. An example of the AiP solution in a low-temperature cofired ceramic (LTCC) process is presented in the 60-GHz band showing an efficiency better than 90%. A major concern with both AoC and AiP solutions is electromagnetic interference (EMI), which is also discussed. Finally, the systems level pros and cons of both AoC and AiP solutions are highlighted from the electrical and economic perspectives for system designers.