The key objective of this paper is to explore the recent state-of-the-art artificial intelligence (AI) applications on the broad field of beamforming. Hence, a multitude of AI-oriented beamforming studies are thoroughly investigated in order to correctly comprehend and profitably interpret the AI contribution in the beamforming performance. Starting from a brief overview of beamforming, including adaptive beamforming algorithms and direction of arrival (DOA) estimation methods, our analysis probes further into the main machine learning (ML) classes, the basic neural network (NN) topologies, and the most efficient deep learning (DL) schemes. Subsequently, and based on the prior aspects, the paper explores several concepts regarding the optimal use of ML and NNs either as standalone beamforming and DOA estimation techniques or in combination with other implementations, such as ultrasound imaging, massive multiple-input multiple-output structures, and intelligent reflecting surfaces. Finally, particular attention is drawn on the realization of beamforming or DOA estimation setups via DL topologies. The survey closes with various important conclusions along with an interesting discussion on potential future aspects and promising research challenges.