It is difficult to understand data and statistical models in high-dimensional space. One way to approach the problem is conditional visualisation, but methods in this area have lagged behind the considerable advances in statistical modelling in recent decades. This thesis presents a new approach to conditional visualisation which uses interactive computer graphics, and supports the exploration of a broad range of statistical models. The new approach to conditional visualisation consists of visualising a single lowdimensional section at a time, showing fitted models on the section, and enhancing the section by displaying observed data which are near the section according to a similarity measure. Two ways of choosing sections are given |choosing sections interactively using data summary graphics, and choosing sections programmatically according to some criteria. The visualisations in this thesis necessitate interactive graphics, which are implemented in the condvis package in R.