Most of the universe today is composed of invisible dark matter (DM) and dark energy. All the instruments constructed by the human civilization so far can detect only 4.6% of the total content of the universe. Existence of the dark components are inferred by their gravitational effects. DM makes up the underlying structure of the universe and constitutes 23% of the total composition. It serves as an invisible scaffolding on which everything we can see lies. Without the additional gravitational pull of DM, the centrifugal force on stars and galaxies would not be balanced out, hence galaxies and clusters of galaxies, i.e. large scale structures, would fly apart. DM keeps falling from all directions into the gravitational potential wells of large scale structures. As it sloshes in and out within smooth potential wells, the phase space distribution of the particles is characterized everywhere by a set of discrete flows. The particles in the flows spontaneously pile up at certain locations, forming caustics which are generically surfaces enveloping the regions with two extra flows. The density distribution must have sharp increases (bumps) at the locations of caustics. Minimal caustic structure is classified as ``outer caustics'' and ``inner caustics.'' The outer caustics are simple fold catastrophes located on topological spheres surrounding the large scale structures. The inner caustics are rings. A caustic ring is a closed tube (like a doughnut) whose transverse cross-section is an elliptic umbilic catastrophe. Evidences have been found for the existence of DM caustics. I discuss our interpretation of the recent gravitational lensing observations of Jee et al. as first evidence for a caustic ring of DM in a galaxy cluster.