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We address the difficult problem of catching in-flight objects with uneven shapes. This requires the solution of three complex problems: accurate prediction of the trajectory of fastmoving objects, predicting the feasible catching configuration, and planning the arm motion, and all within milliseconds. We follow a programming-by-demonstration approach in order to learn, from throwing examples, models of the object dynamics and arm movement. We propose a new methodology to find a feasible catching configuration in a probabilistic manner. We use the dynamical systems approach to encode motion from several demonstrations. This enables a rapid and reactive adaptation of the arm motion in the presence of sensor uncertainty. We validate the approach in simulation with the iCub humanoid robot and in real-world experiments with the KUKA LWR 4+ (7-degree-of-freedom arm robot) to catch a hammer, a tennis racket, an empty bottle, a partially filled bottle, and a cardboard box.