Quality of machined products is often related to the shapes of surfaces that are constrained by geometric tolerances. In this case, statistical quality monitoring should be used to quickly detect unwanted deviations from the nominal pattern. The majority of the literature has focused on statistical profile monitoring, while there is little research on surface monitoring. This paper faces the challenging task of moving from profile to surface monitoring. To this aim, different parametric approaches and control charting procedures are presented and compared with reference to a real case study dealing with cylindrical surfaces obtained by lathe-turning. In particular, a novel method presented in this paper consists of modeling the manufactured surface via Gaussian processes models and monitor the deviations of the actual surface from the target pattern estimated in Phase I. Regardless of the specific case study in this paper, the proposed approach is quite general and can be easily extended to deal with different kinds of surface or profiles.