We present the state of the art on the study of surfaces and tenuous atmospheres of the icy Galilean satellites Ganymede, Europa and Callisto, from past and ongoing space exploration conducted with several spacecraft to recent telescopic observations, and we show how the ESA JUICE mission plans to explore these surfaces and atmospheres in detail with its scientific payload. The surface geology of the moons is the main evidence of their evolution and reflects the internal heating provided by tidal interactions. Surface composition is the result of endogenous and exogenous processes, with the former providing valuable information about the potential composition of shallow subsurface liquid pockets, possibly connected to deeper oceans. Finally, the icy Galilean moons have tenuous atmospheres that arise from charged particle sputtering affecting their surfaces. In the case of Europa, plumes of water vapour have also been reported, whose phenomenology at present is poorly understood and requires future close exploration. In the three main sections of the article, we discuss these topics, highlighting the key scientific objectives and investigations to be achieved by JUICE. Based on a recent predicted trajectory, we also show potential coverage maps and other examples of reference measurements. The scientific discussion and observation planning presented here are the outcome of the JUICE Working Group 2 (WG2): "Surfaces and Near-surface Exospheres of the Satellites, dust and rings".