This thesis deals with the problem of visibility culling in interactive three-dimensional environments. Included in this thesis is a discussion surrounding the issues involved in both constructing and rendering three-dimensional environments. A renderer must sort the objects in a three-dimensional scene in order to draw the scene correctly. The Binary Space Partitioning (BSP) algorithm can sort objects in three-dimensional space using a tree based data structure. This thesis introduces the BSP algorithm in its original context before discussing its other uses in three-dimensional rendering algorithms. Constructive Solid Geometry (CSG) is an efficient interactive modeling technique that enables an artist to create complex three-dimensional environments by performing Boolean set operations on convex volumes. After providing a general overview of CSG, this thesis describes an efficient algorithm for computing CSG expression trees via the use of a BSP tree. When rendering a three-dimensional environment, only a subset of objects in the environment is visible to the user. We refer to this subset of objects as the Potentially Visible Set (PVS). This thesis presents an algorithm that divides an environment into a network of convex cellular volumes connected by invisible portal regions. A renderer can then utilize this network of cells and portals to compute a PVS via a depth first traversal of the scene graph in real-time. Finally, this thesis discusses how a simulation engine might exploit this data structure to provide dynamic collision detection against the scene graph.