This talk will give an overview of astrophysical and cosmological evidence for Dark Matter. While this will make it clear that Dark Matter does exist, it remains entirely unknown what it is made of. Many well-motivated models predict Dark Matter particles with masses between
10 and 10,000 proton masses. Various techniques exist to tackle the search for such particles. This talk will present XENON1T, the most sensitive experiment ever built to search for Dark Matter scattering off a laboratory target. Given availability, new results from XENON1T will be presented. An outlook will be given over a variety of searches that are possible with XENON1T, from unconventional forms of Dark Matter to neutrinos from the Sun and supernova explosions anywhere in the Milky Way.