We trap atoms in versatile two-dimensional (2D) arrays of optical potentials, prepare flexible 2D spin configurations, perform site-selective coherent manipulation, and demonstrate the implementation of simultaneous measurements of different system properties, such as dephasing and decoherence. This novel approach for the flexible manipulation of atomic quantum systems is based on the combination of 2D arrays of microlenses and 2D arrays of liquid crystal light modulators. It offers novel types of control for the investigation of quantum degenerate gases, quantum information processing, and quantum simulations.PACS numbers: 37.10. Jk, 42.50.Ct, Optical dipole potentials such as optical lattices or arrays of focused laser beams provide flexible geometries for the synchronous investigation of multiple atomic quantum systems, as studied e.g in the fields of quantum degenerate gases or quantum information processing with atoms [1][2][3][4][5][6]. In comparison, optical lattices provide a larger number of potential wells (up to 10 6 ) [1][2][3], but the required ability of performing flexible site-selective addressing is still a challenge [7][8][9][10]. On the other hand, architectures based on two-dimensional arrays of tightly focused laser beams inherently provide the ability to address single sites [4,5,11] at the expense of a smaller number of wells (up to several 10 4 ) and a larger separation of sites (typically several µm). Significant future progress is expected from complementing the advantages of these configurations, namely the scalability and the ability to perform quantum operations in parallel, with an additional versatility by achieving reconfigurable, siteselective initialization, manipulation, and detection of individual quantum systems at each site. In this work, we introduce and experimentally implement a novel approach towards this goal: we trap and coherently manipulate two-dimensional (2D) sets of atomic quantum systems in flexible and reconfigurable architectures. We combine 2D arrays of microlenses with perpixel addressable spatial light modulators (SLM) (Fig. 1). This results in reconfigurable, per-site addressable 2D arrays of diffraction-limited laser foci in the focal plane of the microlens array. By re-imaging we reduce the structure (separation 55 µm, spot size 3.7 µm) while maintaining diffraction-limited performance. Although our current setup is limited to a minimum structure size of about 1.3 µm by its numerical aperture (NA), with optics of sufficiently high NA [7,9,10], 2D arrays of laser foci with sub-micron stucture size can be achieved. Thus, our approach allows to create two-dimensional arrays of optical micro-potentials for combined trapping and addressing purposes but also for matching sub-micron-period optical lattices with a flexible system for 2D site-selective addressing.On the next pages, we present versatile trap configurations produced in a robust fashion and demonstrate the ability to allocate atoms in flexible sets of dipole traps with each trap controlled separatel...