Quality monitoring in Additive Manufacturing (AM) is currently mostly based on temperature measurements of the process zone or on layer/piecewise high-resolution surface imaging. To this aim, various sensors, such as pyrometers, photodiodes, and matrix CCD detectors, have been tested. These standard temperature measurements, however, do not provide a comprehensive description of the process dynamics, as they are just limited to surface observations. Furthermore, they are often used for post-factum inspection, i.e., after the piece is partially or even completely produced. No robust and low-cost methods are so far known to monitor the quality of laser processes in real-time. To close this gap, we propose an innovative approach for online quality monitoring of additive manufacturing employing acoustic emissions (AE). In fact, AE signals can provide in-depth information about the process, e.g., melting, resolidification, delamination, and cracking of the workpiece. Moreover, the sintering or melting of the metal powder has several unique acoustic signatures that can be detected and interpreted in terms of quality. In our approach, the correlation of the acoustic signals to the quality of the produced pieces is made by Artificial Intelligence (AI) methods. Specifically, AI in the form of Machine Learning is used to perform a data-driven extraction and recognition of the unique acoustic signatures from different sintering or melting events. In this contribution, we present a summary of our results in the fields of selective laser melting and laser welding, which have similar underlying mechanisms. At first, we discuss how, by using AE, we can classify different types of defects and porosity content in both processes. Afterward, with the aid of high-speed X-ray imaging, we demonstrate the real-time performance of our approach in the classification of transient events/regimes that are critical for the final quality -in particular conduction, stable keyhole, unstable keyhole, pore formation, and blowout. Finally, we present the future possibilities in terms of control of AM processes based on AI.