In this thesis some new, nonparametric methods are introduced to explore uni- or bivariate data. First, we introduce the "shorth plot", a graphical method to depict the main features of one-dimensional probability distributions. Second, we define the "Half-Half plot", a useful… tool for analyzing regression data. Furthermore, a test for spherical symmetry in an empirical likelihood framework is presented. For all methods the asymptotic behavior is derived. The good performance of the methods is demonstrated through simulated and real data examples.