Ultrasound mid-air haptics (UMH) aims to improve natural gestures and interactions by rendering tactile sensations directly in mid-air. It offers a rich design space, while relying on complex acoustic phenomena whose perceptual implications remain understudied. In this thesis, we advance the field by investigating the underlying questions of UMH from the perspectives of perception, rendering, and interactions. We first study the low-level perception of UMH stimuli by conducting the first nerve recordings for UMH, characterizing afferent responses on both glabrous and hairy skin. We then propose a novel shape rendering algorithm, validated through psychophysical studies. Next, we examine skin biomechanics under UMH stimulation to develop new physics-based rendering primitives, demonstrated in more complex shape rendering studies. We then introduce a formal framework for UMH rendering, defining the key components of sampling strategies and intersection strategies for rendering interactions with 3D objects. We also demonstrate through perception studies that the choice of these strategies significantly alters the perceived properties of virtual objects. Finally, we address UMH in virtual reality interactions by proposing and evaluating UMH-based hand position and orientation guidance techniques, exploring visuo-haptic coupling for interpenetration feedback, and discussing bimanual UMH coupling schemes for manipulations scenarios.