The 5G wireless revolution presents some dramatic challenges to the design of handsets and communication infrastructures, as 5G targets higher than 10 Gbps download speed using millimeter-wave (mm-Wave) spectrum with multiple-input multiple-output (MIMO) antennas, connecting densely deployed wireless devices for Internet-of-Everything (IoE), and very small latency time for ultrareliable machine type communication, etc. The broadband modulation bandwidth for 5G RF transmitters (i.e., maximum possibly even above 1 GHz) demands high-power efficiency and stringent linearity from its power amplifier (PA). Additionally, the phased-array MIMO antennas with numerous RF front-ends (RFFEs) will require unprecedented high integration level with low cost, making the design of 5G PA one of the most challenging tasks. As the centimeter-wave (cm-Wave) 5G systems will probably be deployed on the market earlier than their mm-Wave counterparts, we will review in this paper the latest development on 15 GHz and 28 GHz 5G cm-Wave PAs extensively, while also covering some key mm-Wave PAs in the literature. Our review will focus on the available options of device technologies, novel circuit and system architectures, and efficiency enhancement techniques at power back-off for 5G PA design.