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Beamforming is evidently a core technology in recent generations of mobile communication networks. Nevertheless, an iterative process is typically required to optimize the parameters, making it ill-placed for real-time implementation due to high complexity and computational delay. Heuristic solutions such as zero-forcing (ZF) are simpler but at the expense of performance loss. Alternatively, deep learning (DL) is well understood to be a generalizing technique that can deliver promising results for a wide range of applications at much lower complexity if it is sufficiently trained. As a consequence, DL may present itself as an attractive solution to beamforming. To exploit DL, this article introduces general data- and model-driven beamforming neural networks (BNNs), presents various possible learning strategies, and also discusses complexity reduction for the DL-based BNNs. We also offer enhancement methods such as training-set augmentation and transfer learning in order to improve the generality of BNNs, accompanied by computer simulation results and testbed results showing the performance of such BNN solutions.