Catastrophes, or caustics, are abrupt changes in the behavior of a system, which occur as one or more of its control parameters are changed continuously. Some examples include the bright curves of light at the bottom of swimming pools, or the cusp feature at the bottom of an empty cup. We experimentally observe first-order (fold) and second-order (cusp) catastrophes in the density of an atomic cloud as it is dropped and reflected off an optical barrier in the presence of gravity. These phenomena, the cusp in particular, enable field-free refocusing of the expanding atomic cloud and can be harnessed as a tool for manipulation of cold atoms in experimental systems. The structural stability of catastrophes provides inherent robustness against variations in the system’s dynamics and initial conditions, making them suitable for manipulation of atoms under imperfect conditions. [1] S. Rosenblum, O. Bechler, I. Shomroni, R. Kaner, T. Arusi-Parpar, O. Raz, and B. Dayan, "Demonstration of Fold and Cusp Catastrophes in an Atomic Cloud Reflected from an Optical Barrier in the Presence of Gravity", Phys. Rev. Lett. 112, 120403 (2014).