Haptic augmented reality (AR) enables the user to feel a real environment augmented with synthetic haptic stimuli. This article addresses two important topics in haptic AR. First, a new taxonomy for haptic AR is established based on a composite visuo-haptic reality-virtuality continuum extended from the conventional continuum for visual AR. Previous studies related to haptic AR are reviewed and classified using the composite continuum, and associated research issues are discussed. Second, the feasibility of haptically modulating the feel of a real object with the aid of virtual force feedback is investigated, with the stiffness as a goal haptic property. All required algorithms for contact detection, stiffness modulation, and force control are developed, and their individual performances are thoroughly evaluated. The resulting haptic AR system is also assessed in a psychophysical experiment, demonstrating its competent perceptual performance for stiffness modulation. To our knowledge, this work is among the first efforts in haptic AR for systematic augmentation of real object attributes with virtual forces, and it serves as an initial building block toward a general haptic AR system. Finally, several research issues identified during the feasibility study are introduced, with the aim of eliciting more research interest in this exciting yet unexplored area.