This talk will present our effort to control and use the dipole-dipole interactions between cold atoms in order to implement spin Hamiltonians useful for quantum simulations of situations encountered in condensed matter or in the many-body problem. We have developed a platform where we trap individual atoms in arrays of optical tweezers separated by a few micrometers. We create almost arbitrary geometries of the atomic arrays in two and three dimensions up to about 200 atoms. To make the atoms interact, we excite them to Rydberg states where they develop strong interactions even at long distance. Using this platform, we have in particular explored some aspects of quantum magnetism and topological synthetic quantum matter.