Glacial Isostatic Adjustment (GIA) modelling has recently seen a significant development, stimulated by the need of understanding past, current and future sea levelvariations and geodetic signals associated with climate change. Our main motivation is that albeit its importance is well recognized within the climate science community, the problem of classifying and quantifying GIA modelling uncertainties has so far received little attention. Here, we consider two possible ways of defining and evaluating these uncertainties. The first is associated with limited knowledge of input model parameters (e.g. the viscosity profile of the Earth's mantle or the deglaciation history), once it is assumed that the ice margins are known and a unique set of relative sea level (RSL) data are used to constrain the model. We also discuss a second and more problematic source of uncertainty, associated with structural differences in GIA models, stemming from distinct eustatic curves and ice margins geometries, different RSL constraints, non-identical input parameters and different numerical solution schemes. By analysing the present-day GIA fingerprints' of relative and absolute sea levelchange, and exploring the GIA contribution to secular sea levelrise and to the time-variations of the Earth's gravity field, here we evaluate the two types of uncertainty showing that they are (i) of significant amplitude and (ii) of comparable importance.