Given a set of multidimensional points, the skyline operator returns a set of potentially interesting points from such a dataset. This popular operator filters out a set of tuples that are not dominated by other ones, reducing the size of a possibly large initial dataset. However, with the dataset dimensions growing, the query result of the skyline operator can have a high cardinality that could overwhelm the final user looking at the result, yielding the very opposite goal. Moreover, it doesn't allow any user to express their preferences over the attributes, in order to control the dataset cardinality and to return a more satisfying result. In this survey, we discuss and compare the more recent approaches developed to extend the skyline operator's functionalities, and we discuss their applicability in real-world scenarios. We show how these frameworks operate on the dataset and how they claim to mitigate the drawbacks coming from the skyline operator.