This paper addresses the millimeter-wave antenna design aspect of the future 5G wireless systems. The paper reviews the objectives and requirements of millimeter-wave antennas for 5G. Recent advances in mm-wave antenna are reported and design guidelines are discussed. In particular, four different designs are identified from the recent literature based on their attractive characteristics that support 5G requirements and applications. The first design employs a dual-band slotted patch antenna operating at 28 GHz and 38 GHz. The antenna has circular polarization and is excited by a single-feed microstrip line. The present design is desirable for high-gain antenna array implementation in the mm-wave band, in order to compensate for the mm-wave propagation loss. The second design that is presented employs a compact planar inverted-F antenna (PIFA) with single layer dielectric load of a superstrate to enhance the gain and achieve a wide impedance bandwidth resulting in high efficiency. The third design that operates in the mm-wave band is a T-Shaped patch antenna. The proposed antenna a wideband range from (26.5 GHz-40 GHz) of the Ka band. The PFT substrate was used as it offers some advantages; low cost, high flexibility, harmless to human body and resistive towards environmental effects. The last mm-wave antenna design presented employs two MEMO arrays each composed of 2×2 antenna elements. The two MIMO array configurations are spatially orthogonal to each other which results in polarization diversity.