The massive increase in the number of connected devices is making it necessary to use higher frequencies and wider bandwidths. The use of frequencies in the 20-300 GHz will enable achieving higher capacities and data rates. In order to compensate for the higher free-space path loss and increased atmospheric absorption directive antenna elements have to be used and, thus, beam-steering and beam-forming capabilities are needed. In this thesis, mm-wave antennas in the 24-35 GHz range are developed. The designs include both mobile phone and base station antennas since both of them will have to evolve to meet the demands of 5G networks. The first part of this thesis focuses on finding mm-wave antenna solutions for 5G mobile handsets. The mobile phone antennas radiate towards the end-fire direction with respect to the mobile phone. The designs present dual-polarized operation and wide-angle beam-steering for increased reliability. Moreover, the mm-wave antennas are designed so that they do not heavily degrade the performance of the already present sub-6 GHz antennas. The proposed solutions include 3 and 4-element arrays which are either integrated in the metal frame of the mobile phone, or radiate through a small window in it. The second part of this thesis introduces 5G base station antennas and their challenges. The base station antennas presented are scalable in the number of antenna elements in order to adapt to different use cases. Moreover, and as a huge amount of base stations are going to be required with the development of 5G, the antennas are energy efficient and relatively cheap to manufacture. They present beam-steering or beam-switching capabilities in order to keep track of the mobile users, as well as high directivity. The designs presented include an efficient 16-element horn antenna phased-array, and a wide-angle dual-polarized beam-switching lens antenna.