Like every other field of intellectual endeavor, astronomy is being revolutionized by the advances in information technology. There is an ongoing exponential growth in the volume, quality, and complexity of astronomical data sets, mainly through large digital sky surveys and archives. The Virtual Observatory (VO) concept represents a scientific and technological framework needed to cope with this data flood. Systematic exploration of the observable parameter spaces, covered by large digital sky surveys spanning a range of wavelengths, will be one of the primary modes of research with a VO. This is where the truly new discoveries will be made, and new insights be gained about the already known astronomical objects and phenomena. We review some of the methodological challenges posed by the analysis of large and complex data sets expected in the VO-based research. The challenges are driven both by the size and the complexity of the data sets (billions of data vectors in parameter spaces of tens or hundreds of dimensions), by the heterogeneity of the data and measurement errors, including differences in basic survey parameters for the federated data sets (e.g., in the positional accuracy and resolution, wavelength coverage, time baseline, etc), various selection effects, as well as the intrinsic clustering properties (functional form, topology) of the data distributions in the parameter spaces of observed attributes. Answering these challenges will require substantial collaborative efforts and partnerships between astronomers, computer scientists, and statisticians.