Low-Gain Avalanche Diodes are a recently-developed class of silicon sensors. Characterized by an internal moderate gain that enhances the signal amplitude and if built on thin silicon substrates of a few tens of microns, they feature fast signals and exhibit excellent timing performance. Thanks to their fast timing they are planned to be exploited in timing detectors in High-Energy Physics experiments, for example for the upgrades of the ATLAS and CMS detectors at the High Luminosity Large Hadron Collider (HL-LHC) at CERN. However, to achieve a spatially uniform multiplication a large pixel pitch is needed, preventing a fine spatial resolution. To overcome this limitation, the AC-coupled LGAD approach was introduced. In this type of device, metal electrodes are placed over an insulator at a fine pitch, and signals are capacitively induced on these electrodes. The fabrication technology is similar for the two LGAD families, although a fine tuning of a few process parameters needs to be carefully studied. Other R&D efforts towards detectors that can simultaneously provide good time and spatial resolution, based on the LGAD concept, are under way. These efforts aim also to mitigate the loss of performance at high irradiation fluences due to the acceptor removal within the gain layer. In this paper we describe the main points in the fabrication of LGADs and AC-LGADs in a clean-room. We also discuss novel efforts carried on related topics.