Surface characterization tools such as scanning probe microscopy (SPM) and scanning electron microscopy are widely used to study materials prepared by electrodeposition. However, with the exception of detailed in-situ SPM and X-ray investigations of single-crystal surfaces, such studies are often predominantly qualitative. Few quantitative data are reported for the surface morphology of polycrystalline electrodeposited films apart from e.g. the sample-averaged surface roughness. Nevertheless, it is straightforward to extract other parameters such as the length-scale dependent surface roughness or the local surface slope. Here we discuss the insights that can be gained from such studies of Cu films electrodeposited at different potentials, with different additives and under different mass transport conditions, including recent data for pulse-deposition.