One of the key ingredients of the standard model of Cosmology is dark matter. The existence of dark matter has been established from numerous astrophysical and cosmological observations, but its interaction nature still remains enigmatic. Assuming dark matter is a single particle thermal relic, a canonical paradigm of dark matter with a prediction of its interaction cross section with the standard model particles is developed. Miraculously, the size of the estimated cross section is just within the range of current experiments, encouraging various searches to look for the direct interaction of dark matter with the visible matter. However, after more than a generation of experiments, no unambiguous signature of dark matter has been detected, and most of the targeted parameter space proposed by the single particle thermal relic is excluded. As a result, we are led to move away from the simple single particle thermal relic paradigm and explore alternative scenarios. Here, four alternative dark matter frameworks are discussed and their phenomenological signature are explored. 1) There is another particle in the dark sector near degenerate with the dark matter that has efficient annihilation rate to the standard model; whereas the dark matter itself has inefficient annihilation rate to the standard model states.  2) Dark matter annihilates to a pair of meta-stable mediators, which subsequently decay to standard model particles.  3) Dark matter is asymmetric and its relic abundance is set by annihilating away the symmetric component. 4) Dark matter is decoupled from the photon thermal sector and has negligible initial abundance; but then gets populated through its feeble interaction with the standard model.  All of these scenarios, can successfully produce the right relic density of dark matter with `natural' size couplings, while being safe from the current experimental bounds. Furthermore, some of these models have clear phenomenological signatures within the reach of the next generation experiments.