Braking device for a wind turbine comprising a shaft, which is associated with a rotor, and a brake disk, which is associated with the shaft and coupled thereto for conjoint rotation, or for a wind turbine comprising a nacelle, which holds and supports a rotor, and comprising a support tower for the nacelle, the nacelle being mounted rotatably about an axis relative to the support tower, the braking device being designed to fix the nacelle relative to the support tower in a selectable rotational position, the braking device comprising a brake piston, the brake piston being able to be advanced against the brake disk or the brake piston being able to be arranged either on the nacelle or on the support tower and being able to be adjusted against a counter bearing on the other part in order to exert the braking force, characterized in that the brake piston has a tubular portion having a longitudinal central axis and having one of the brake disk or the end face facing the counter bearing and having a through-opening, and in that the tubular portion of the brake piston is designed for longitudinally displaceable guidance in a cylinder chamber accommodating the brake piston, and in that in the through-opening in the region of the end face of the tubular portion, an annular holding and supporting part is inserted in a fixed or longitudinally displaceable manner relative to the tubular portion, and in that the holding and supporting part has a dome-shaped bearing surface radially on the inside for supporting a brake pad carrier part, and in that the brake pad carrier part has a dome-shaped counter-bearing surface which is complementary to the bearing surface, so that the brake pad carrier part is pivotably mounted and held relative to the holding and supporting part, and in that the holding and supporting part having its dome-shaped bearing surface is arranged completely within the tubular portion of the brake piston in the direction of the longitudinal central axis. the braking device comprising a brake piston, the brake piston being able to be advanced against the brake disk or the brake piston being able to be arranged either on the nacelle or on the support tower and being able to be adjusted against a counter bearing on the other part in order to exert the braking force, characterized in that the brake piston has a tubular portion having a longitudinal central axis and having one of the brake disk or the end face facing the counter bearing and having a through-opening, and in that the tubular portion of the brake piston is designed for longitudinally displaceable guidance in a cylinder chamber accommodating the brake piston, and in that in the through-opening in the region of the end face of the tubular portion, an annular holding and supporting part is inserted in a fixed or longitudinally displaceable manner relative to the tubular portion, and in that the holding and supporting part has a dome-shaped bearing surface radially on the inside for supporting a brake pad carrier part, and in that the brake pad carrier part has a dome-shaped counter-bearing surface which is complementary to the bearing surface, so that the brake pad carrier part is pivotably mounted and held relative to the holding and supporting part, and in that the holding and supporting part having its dome-shaped bearing surface is arranged completely within the tubular portion of the brake piston in the direction of the longitudinal central axis.