We analyse some properties of circumplanetary discs. Flow through such discs may provide most of the mass to gas giant planets, and such discs are likely sites for the formation of regular satellites. We model these discs as accretion discs subject to the tidal forces of the central star. The tidal torques from the star remove the disc angular momentum near the disc outer edge and permit the accreting disc gas to lose angular momentum at the rate appropriate for steady accretion. Circumplanetary discs are truncated near the radius where periodic ballistic orbits cross, where tidal forces on the disc are strong. This radius occurs at approximately 0.4rH for the planet Hill radius rH. During the T Tauri stage of disc accretion, the disc is fairly thick with aspect ratio H/r≳ 0.2 and the disc edge tapering occurs over a radial scale ∼H∼ 0.1rH. The disc fluid equations can be rescaled in the Hill approximation to a form similar to the flow equations for a disc in a binary star system with a mass ratio of unity. For a circular or slightly eccentric orbit planet, no significant resonances lie within the main body of the disc. Tidally driven waves involving resonances none the less play an important role in truncating the disc, especially when it is fairly thick. We model the disc structure using one-dimensional time-dependent and steady-state models and also two-dimensional smoothed particle hydrodynamics simulations. The circumplanetary disc structure depends on the variation of the disc turbulent viscosity with radius and is insensitive to the angular distribution of the accreting gas. Dead zones may occur within the circumplanetary disc and result in density structures. If the disc is turbulent throughout, the predicted disc structure near the location of the regular Jovian and Saturnian satellites is smooth with no obvious feature that would favour formation at their current locations. It may be possible that substructure, such as due to variations in the disc turbulence, could lead to the trapping of migrating satellites.