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 simulation of condensed matter or quantum optics situations. 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 either excite them to Rydberg states or induce optical dipoles with a near-resonance laser. Using this platform, we have in particular explored quantum magnetism, topological synthetic quantum matter, and a new light-matter interface.