Hyperbolic experiences are forms of intensification in which what is revealed transcends itself. Hyper-phenomena cross thresholds of the foreign without overcoming them. They appear in many shapes. As the infinite, the impossible, the invisible, or the unforgettable, they break the boundaries of experience. In the open forms of gift, representation, trust, and hospitality, they weave social threads that slip away from normative regulation and threaten to tear apart in the excesses of violence. In the strangeness of the religious, transcendence achieves its own, yet also contentious, weight. Methodologically, hyperbolic phenomena demand an indirect description that reveals what eludes direct access. They operate at the edges of phenomenology.