I will give a short introduction to Dark Matter physics. First, I will sum up the the main evidences of Dark Matter from the Galactic to large cosmological scales pointing out very recent developments and ideas. So far the evidences are only gravitational. Surprisingly, even the gravitational observables of Dark Matter can hint about 'beyond-gravitational nature' of Dark Matter. The very special role of the revealing this have the Gaia experiment already publishing the first data and the EUCLID experiment in longer term. Beyond gravitation, we have many experimental constraints on the ‘particle’ nature of Dark Matter and so far only few questionable hints of Dark Matter. The constraining experiments involve the accelerator (LHC at CERN), underground (‘direct detection') and cosmic experiments (‘indirect detection’). The strongest possible hint comes by gamma-rays from the Galactic Centre, the ‘Galactic Centre excess’ at 2-6 GeV found in the data of the Fermi LAT experiment. However, due to rapidly increasing experimental bounds the mainstream candidate of Dark Matter, Weakly Interacting Massive Particle (WIMP), is losing its ground. I will point out interesting escape scenarios of WIMP and highlight some alternatives for WIMPy Dark Matter.
