The role of transformations in modeling data groups is investigated. First, situations with known finite sets of possible transformations are considered. Such transformations can occur in the presence of observations from the same class recorded in different ways. This effect can occur because of recording inconsistencies due to the use of different scales, operator errors, or simply various recording styles. The idea presented in the talk aims to alleviate this issue through modifications incorporated into mixture models. Next, transformations are considered in a more general setting with applications to modeling skewed data. Several simulation studies and applications to real-life data sets are considered.