This paper reviews recent advances in the design of low noise amplifier (LNA) in complementary metal oxide semiconductor (CMOS) technology for radio transceivers at microwave and millimeter wave (mmWave) frequencies. First, the evolution of wireless communication systems and CMOS technology are briefly revisited to highlight the requirements of an LNA design. Then, key performance parameters and device circuit models are described. Next, we discuss typical LNA topologies, followed by those important design techniques, algorithms and concepts developed specifically for CMOS LNAs. Moreover, reported CMOS LNA designs are summarized, and future design issues are identified. Finally, we conclude the paper and briefly outline our future work on CMOS LNA designs.