Visible light communication (VLC) allows the dual use of light-emitting diodes (LEDs) for wireless communication purposes in addition to their primary purpose of illumination. As in any other communication system, realistic channel modelling is a key for VLC system design, analysis and testing. In this paper, we present a comprehensive survey of indoor VLC channel models. In order to set the background, we start with an overview of infrared (IR) channel modelling, which has received much attention in the past, and highlight the differences between visible and IR optical bands. In the light of these, we present a comparative discussion of existing VLC channel modelling studies and point out the relevant advantages and disadvantages. Then, we provide a detailed description of a site-specific channel modelling approach based on non-sequential ray tracing that precisely captures the optical propagation characteristics of a given indoor environment. We further present channel models for representative deployment scenarios developed through this approach that were adopted by the Institute of Electrical and Electronics Engineering (IEEE) as reference channel models. Finally, we consider mobile VLC scenarios and investigate the effect of receiver location and rotation for a mobile indoor user. This article is part of the theme issue 'Optical wireless communication'.