Functional data analysis has been the subject of increasing interest over the past decades. Most existing theoretical contributions assume that the curves are fully observed, whereas in practice the data are observed on a finite grid and may be affected by noise. To account for the presence of noise and discretization, it is common to smooth the data. The purpose of this paper is to review some of the recent works studying the influence of the observation scheme for estimating the mean and principal components. Some of this work questions the need to smooth the data when the observation grid is fixed.