The five large moons of Uranus are important targets for future spacecraft missions. To motivate and inform the exploration of these moons, we model their internal evolution, present-day physical structures, and geochemical and geophysical signatures that may be measured by spacecraft. We predict that if the moons preserved liquid until present, it is likely in the form of residual oceans less than 30 km thick in Ariel, Umbriel, Titania, and Oberon. The preservation of liquid strongly depends on material properties and, potentially, on dynamical circumstances that are unknown. Miranda is unlikely to preserve liquid until present unless it experienced tidal heating a few tens of million years ago. The triaxial shapes estimated from Voyager 2 data for Miranda and Ariel further support the prospect that these moons are internally differentiated with a rocky core and icy shell. We find that since the thin residual layers may be hypersaline, their induced magnetic fields could be detectable by future spacecraft-based magnetometers. However, if the ocean is maintained primarily by ammonia, and thus well below the water freezing point, then its electrical conductivity may be too small to be detectable by spacecraft. Lastly, our calculated tidal Love number (k₂) and dissipation factor (Q) are consistent with the Q/k₂ values previously inferred from dynamical evolution models. In particular, we find that the low Q/k₂ estimated for Titania supports the hypothesis that Titania currently holds an ocean.