The coherent manipulation of individual quantum objects organized in arrays is a prerequisite to any scalable quantum information platform. The cumulated efforts to control electron spins in quantum dot arrays have permitted the recent realization of quantum simulators and multielectron spin-coherent manipulations. Although a natural path to resolve complex quantum-matter problems and to process quantum information, two-dimensional (2D) scaling with a high connectivity of such implementations remains undemonstrated. Here we demonstrate the 2D coherent control of individual electron spins in a 3 × 3 array of tunnel-coupled quantum dots. We focus on several key quantum functionalities: charge-deterministic loading and displacement, local spin readout and local coherent exchange manipulation between two electron spins trapped in adjacent dots. This work lays some of the foundations to exploit a 2D array of electron spins for quantum simulation and information processing.