The next generation of cellular wireless communication networks (the much hyped "5G") is targeting a 1000x increase in data capacity. This has sparked an investigation of new and transformative wireless communication paradigms, including massive MIMO, full duplex and millimeter-wave wireless. These new wireless paradigms place requirements on the radio circuitry that are orders of magnitude more challenging than traditional systems, forcing us to rethink conventional radio design. Conventional analog and radio frequency circuit design has relied on linear, time-invariant (LTI) components and circuits. However, LTI components and circuits are restricted in the signal processing functionalities that can be implemented. Recently, there has been significant interest in linear, periodically time varying (LPTV) circuits that can enable new functionalities and components, such as highly-tunable, high quality integrated filters, front-ends with spatio-spectral filtering capability and integrated non-magnetic non-reciprocal components such as circulators and isolators. This paper reviews recent research breakthroughs in LPTV circuits and systems that enable full-duplex and massive MIMO wireless. CCS CONCEPTS • Hardware → Wireless devices; Radio frequency and wireless circuits; 1