We introduce a set of integrated interaction techniques to interpret and interrogate dimensionality-reduced data. Projection techniques generally aim to make a high-dimensional information space visible in form of a planar layout. However, the meaning of the resulting data projections can be hard to grasp. It is seldom clear why elements are placed far apart or close together and the inevitable approximation errors of any projection technique are not exposed to the viewer. Previous research on dimensionality reduction focuses on the efficient generation of data projections, interactive customisation of the model, and comparison of different projection techniques. There has been only little research on how the visualization resulting from data projection is interacted with. We contribute the concept of probing as an integrated approach to interpreting the meaning and quality of visualizations and propose a set of interactive methods to examine dimensionality-reduced data as well as the projection itself. The methods let viewers see approximation errors, question the positioning of elements, compare them to each other, and visualize the influence of data dimensions on the projection space. We created a web-based system implementing these methods, and report on findings from an evaluation with data analysts using the prototype to examine multidimensional datasets.