Functional data are becoming increasingly common in a variety of fields. Many studies underline the importance to consider the representation of data as functions. This has sparked a growing attention in the development of adapted statistical tools that allow to analyze such kind of data : functional data analysis (FDA). The aims of FDA are mainly the same as in the classical statistical analysis, e.g. representing and visualizing the data, studying variability and trends, comparing different data sets, as well as modeling and predicting,... Recent advances in FDA allow to construct different classification methods, based on the comparison between centrality curves or using change points,... We review some procedures that have been used to classify functional data. The main point is to show the good practical behaviors of these procedures on a sample of curves. In addition, theoretical advances on functional estimations related to these classification methods are provided.