Most human-computer interactive systems focus primarily on the graphical rendering of visual information and, to a lesser extent, on the display of auditory information. Haptic interfaces have the potential to increase the quality of human-computer interaction by accommodating the sense of touch. They provide an attractive augmentation to visual display and enhance the level of understanding of complex data sets. A haptic rendering system generates contact or restoring forces to prevent penetration into the virtual objects and create a sense of touch. The system computes contact forces by first detecting if a collision or penetration has occurred. Then, the system determines the (projected) contact points on the model surface. Finally, it computes restoring forces based on the amount of penetration. Researchers have recently investigated the problem of rendering the contact forces and torques between 3D virtual objects. This problem is known as six-degrees-of-freedom (6-DOF) haptic rendering, as the computed output includes both 3-DOF forces and 3-DOF torques. This article presents an overview of our work in this area. We suggest different approximation methods based on the principle of preserving the dominant perceptual factors in haptic exploration.