Superdirective array may achieve an array gain proportional to the square of the number of antennas $M^2$. In the early studies of superdirectivity, little research has been done from wireless communication point of view. To leverage superdirectivity for enhancing the spectral efficiency, this paper investigates multi-user communication systems with superdirective arrays. We first propose a field-coupling-aware (FCA) multi-user channel estimation method, which takes into account the antenna coupling effects. Aiming to maximize the power gain of the target user, we propose multi-user multipath superdirective precoding (SP) as an extension of our prior work on coupling-based superdirective beamforming. Furthermore, to reduce the inter-user interference, we propose interference-nulling superdirective precoding (INSP) as the optimal solution to maximize user power gains while eliminating interference. Then, by taking the ohmic loss into consideration, we further propose a regularized interference-nulling superdirective precoding (RINSP) method. Finally, we discuss the well-known narrow directivity bandwidth issue, and find that it is not a fundamental problem of superdirective arrays in multi-carrier communication systems. Simulation results show our proposed methods outperform the state-of-the-art methods significantly. Interestingly, in the multi-user scenario, an 18-antenna superdirective array can achieve up to a 9-fold increase of spectral efficiency compared to traditional multiple-input multiple-output (MIMO), while simultaneously reducing the array aperture by half.