Light-fidelity (LiFi) is a light-based wireless communication technology which can complement radio-frequency (RF) communication technologies for indoor applications. Although LiFi signals are spatially more contained than RF signals, the broadcasting nature of LiFi also makes it susceptible to eavesdropping. Therefore, it is important to secure the transmitted data against potential eavesdroppers. In this paper, an overview of the recent developments pertaining to LiFi physical layer security (PLS) is provided, and the main differences between LiFi PLS and RF PLS are explained. LiFi achievable secrecy rates and upper bounds are then investigated under practical channel models and transmission schemes. Beamforming and jamming, which received significant research attention recently as a means to achieve PLS in LiFi, are also investigated under indoor illumination constraints. Finally, future research directions of interest in LiFi PLS are identified and discussed. This article is part of the theme issue ‘Optical wireless communication’.